how can I print my equation or configure maple so that they don't try to autofit themselves in the window? and what would the best way to export them to MATLAB be? I know there's the codegeneration command.

For example, I noticed that the output of some commands like StateSpace prints the equations in a way that if they are too long, they won't try tu fit, but rather it lets you scroll to the right:

Is there any command or package in Maple that computes blow ups? I didn't find blow up in the help.

I am coding a big module to solving my project : analyze function in math, but when I compile my module maple return "Error," but it doesn't tell me what error happened.

I check the maple help and it said:" If no msgString is given, error raises the most recently occurring exception" but I have no exception before. 

This is the pic of that error.

Thank for your help.

Dear Maple users,

I have very interesting problem with evaluating of only symbolic equations.

The problem is: (In document mode)
When I try to evaluate all numeric values for example typing 1+2 and press Enter it successfuly evaluates 3.
But when I try to evaluate symbolic values for example x + y nothing happens.

I tried lots of things to solve this, but no luck.
Shortly if the equation contains only numbers it evaluates successfuly.
And if the equation contains one or more symbolic variables like (x, y, z, variable1, test1), it does nothing.

What could be the problem?
 

(Because of this problem I cannot use the document mode, so I'm using the worksheet mode. Worksheet mode works good, but sometimes it is not calculating like document mode)

System is Windows 7 x64
Maple 2016
8 x 3.50GHz Xeon CPU
128 GB RAM
Windows Language is Turkish, (I tried with also USA English, but no luck either)
Keyboard is Turkish TR, (I tried with also US English, but no luck either)

Please I am having problem with this code particularly the last subroutine

#subroutine 1

restart;
Digits:=30:

f:=proc(n)
    -25*y[n]+12*cos(x[n]):
end proc:

#subroutine 2

e1:=y[n+4] = -y[n]+2*y[n+2]+((1/15)*h^2+(2/945)*h^2*u^2+(1/56700)*h^2*u^4-(1/415800)*h^2*u^6-(167/833976000)*h^2*u^8-(2633/245188944000)*h^2*u^10-(2671/5557616064000)*h^2*u^12-(257857/13304932857216000)*h^2*u^14-(3073333/4215002729166028800)*h^2*u^16)*f(n)+((16/15)*h^2-(8/945)*h^2*u^2-(1/14175)*h^2*u^4+(1/103950)*h^2*u^6+(167/208494000)*h^2*u^8+(2633/61297236000)*h^2*u^10+(2671/1389404016000)*h^2*u^12+(257857/3326233214304000)*h^2*u^14+(3073333/1053750682291507200)*h^2*u^16)*f(n+1)+((26/15)*h^2+(4/315)*h^2*u^2+(1/9450)*h^2*u^4-(1/69300)*h^2*u^6-(167/138996000)*h^2*u^8-(2633/40864824000)*h^2*u^10-(2671/926269344000)*h^2*u^12-(257857/2217488809536000)*h^2*u^14-(3073333/702500454861004800)*h^2*u^16)*f(n+2)+((16/15)*h^2-(8/945)*h^2*u^2-(1/14175)*h^2*u^4+(1/103950)*h^2*u^6+(167/208494000)*h^2*u^8+(2633/61297236000)*h^2*u^10+(2671/1389404016000)*h^2*u^12+(257857/3326233214304000)*h^2*u^14+(3073333/1053750682291507200)*h^2*u^16)*f(n+3)+((1/15)*h^2+(2/945)*h^2*u^2+(1/56700)*h^2*u^4-(1/415800)*h^2*u^6-(167/833976000)*h^2*u^8-(2633/245188944000)*h^2*u^10-(2671/5557616064000)*h^2*u^12-(257857/13304932857216000)*h^2*u^14-(3073333/4215002729166028800)*h^2*u^16)*f(n+4):

e2:=y[n+3] = -y[n+1]+2*y[n+2]+(-(1/240)*h^2-(31/60480)*h^2*u^2-(67/1814400)*h^2*u^4-(109/53222400)*h^2*u^6-(18127/186810624000)*h^2*u^8-(64931/15692092416000)*h^2*u^10-(9701/59281238016000)*h^2*u^12-(20832397/3406062811447296000)*h^2*u^14-(11349439/51876956666658816000)*h^2*u^16)*f(n)+((1/10)*h^2+(31/15120)*h^2*u^2+(67/453600)*h^2*u^4+(109/13305600)*h^2*u^6+(18127/46702656000)*h^2*u^8+(64931/3923023104000)*h^2*u^10+(9701/14820309504000)*h^2*u^12+(20832397/851515702861824000)*h^2*u^14+(11349439/12969239166664704000)*h^2*u^16)*f(n+1)+((97/120)*h^2-(31/10080)*h^2*u^2-(67/302400)*h^2*u^4-(109/8870400)*h^2*u^6-(18127/31135104000)*h^2*u^8-(64931/2615348736000)*h^2*u^10-(9701/9880206336000)*h^2*u^12-(20832397/567677135241216000)*h^2*u^14-(11349439/8646159444443136000)*h^2*u^16)*f(n+2)+((1/10)*h^2+(31/15120)*h^2*u^2+(67/453600)*h^2*u^4+(109/13305600)*h^2*u^6+(18127/46702656000)*h^2*u^8+(64931/3923023104000)*h^2*u^10+(9701/14820309504000)*h^2*u^12+(20832397/851515702861824000)*h^2*u^14+(11349439/12969239166664704000)*h^2*u^16)*f(n+3)+(-(1/240)*h^2-(31/60480)*h^2*u^2-(67/1814400)*h^2*u^4-(109/53222400)*h^2*u^6-(18127/186810624000)*h^2*u^8-(64931/15692092416000)*h^2*u^10-(9701/59281238016000)*h^2*u^12-(20832397/3406062811447296000)*h^2*u^14-(11349439/51876956666658816000)*h^2*u^16)*f(n+4):

e3:=h*delta[n] = (-149/42-(16/245)*u^2-(1324/169785)*u^4-(559246/695269575)*u^6-(14310311/175207932900)*u^8-(170868550903/20641246574949000)*u^10)*y[n]+(128/21+(32/245)*u^2+(2648/169785)*u^4+(1118492/695269575)*u^6+(14310311/87603966450)*u^8+(170868550903/10320623287474500)*u^10)*y[n+1]+(-107/42-(16/245)*u^2-(1324/169785)*u^4-(559246/695269575)*u^6-(14310311/175207932900)*u^8-(170868550903/20641246574949000)*u^10)*y[n+2]+(-(67/1260)*h^2+(1241/198450)*h^2*u^2+(277961/366735600)*h^2*u^4+(26460409/333729396000)*h^2*u^6+(1363374533/168199615584000)*h^2*u^8+(16323847966961/19815596711951040000)*h^2*u^10)*f(n)+((188/105)*h^2+(5078/99225)*h^2*u^2+(556159/91683900)*h^2*u^4+(51834031/83432349000)*h^2*u^6+(67782373/1078202664000)*h^2*u^8+(1854079193287/291405833999280000)*h^2*u^10)*f(n+1)+((31/90)*h^2+(341/33075)*h^2*u^2+(79361/61122600)*h^2*u^4+(23456627/166864698000)*h^2*u^6+(1228061399/84099807792000)*h^2*u^8+(14797833720283/9907798355975520000)*h^2*u^10)*f(n+2)+(-(4/105)*h^2-(46/14175)*h^2*u^2-(809/1871100)*h^2*u^4-(27827/567567000)*h^2*u^6-(637171/122594472000)*h^2*u^8-(33500737/62523180720000)*h^2*u^10)*f(n+3)+((1/252)*h^2+(23/28350)*h^2*u^2+(809/7484400)*h^2*u^4+(27827/2270268000)*h^2*u^6+(637171/490377888000)*h^2*u^8+(33500737/250092722880000)*h^2*u^10)*f(n+4):

e4:=y[3] = -y[1]+2*y[2]+(-(1/240)*h^2-(31/60480)*h^2*u^2-(67/1814400)*h^2*u^4-(109/53222400)*h^2*u^6-(18127/186810624000)*h^2*u^8-(64931/15692092416000)*h^2*u^10-(9701/59281238016000)*h^2*u^12-(20832397/3406062811447296000)*h^2*u^14-(11349439/51876956666658816000)*h^2*u^16)*f(0)+((1/10)*h^2+(31/15120)*h^2*u^2+(67/453600)*h^2*u^4+(109/13305600)*h^2*u^6+(18127/46702656000)*h^2*u^8+(64931/3923023104000)*h^2*u^10+(9701/14820309504000)*h^2*u^12+(20832397/851515702861824000)*h^2*u^14+(11349439/12969239166664704000)*h^2*u^16)*f(1)+((97/120)*h^2-(31/10080)*h^2*u^2-(67/302400)*h^2*u^4-(109/8870400)*h^2*u^6-(18127/31135104000)*h^2*u^8-(64931/2615348736000)*h^2*u^10-(9701/9880206336000)*h^2*u^12-(20832397/567677135241216000)*h^2*u^14-(11349439/8646159444443136000)*h^2*u^16)*f(2)+((1/10)*h^2+(31/15120)*h^2*u^2+(67/453600)*h^2*u^4+(109/13305600)*h^2*u^6+(18127/46702656000)*h^2*u^8+(64931/3923023104000)*h^2*u^10+(9701/14820309504000)*h^2*u^12+(20832397/851515702861824000)*h^2*u^14+(11349439/12969239166664704000)*h^2*u^16)*f(3)+(-(1/240)*h^2-(31/60480)*h^2*u^2-(67/1814400)*h^2*u^4-(109/53222400)*h^2*u^6-(18127/186810624000)*h^2*u^8-(64931/15692092416000)*h^2*u^10-(9701/59281238016000)*h^2*u^12-(20832397/3406062811447296000)*h^2*u^14-(11349439/51876956666658816000)*h^2*u^16)*f(4):

e5:=h*delta[0] = (-149/42-(16/245)*u^2-(1324/169785)*u^4-(559246/695269575)*u^6-(14310311/175207932900)*u^8-(170868550903/20641246574949000)*u^10)*y[0]+(128/21+(32/245)*u^2+(2648/169785)*u^4+(1118492/695269575)*u^6+(14310311/87603966450)*u^8+(170868550903/10320623287474500)*u^10)*y[1]+(-107/42-(16/245)*u^2-(1324/169785)*u^4-(559246/695269575)*u^6-(14310311/175207932900)*u^8-(170868550903/20641246574949000)*u^10)*y[2]+(-(67/1260)*h^2+(1241/198450)*h^2*u^2+(277961/366735600)*h^2*u^4+(26460409/333729396000)*h^2*u^6+(1363374533/168199615584000)*h^2*u^8+(16323847966961/19815596711951040000)*h^2*u^10)*f(0)+((188/105)*h^2+(5078/99225)*h^2*u^2+(556159/91683900)*h^2*u^4+(51834031/83432349000)*h^2*u^6+(67782373/1078202664000)*h^2*u^8+(1854079193287/291405833999280000)*h^2*u^10)*f(1)+((31/90)*h^2+(341/33075)*h^2*u^2+(79361/61122600)*h^2*u^4+(23456627/166864698000)*h^2*u^6+(1228061399/84099807792000)*h^2*u^8+(14797833720283/9907798355975520000)*h^2*u^10)*f(2)+(-(4/105)*h^2-(46/14175)*h^2*u^2-(809/1871100)*h^2*u^4-(27827/567567000)*h^2*u^6-(637171/122594472000)*h^2*u^8-(33500737/62523180720000)*h^2*u^10)*f(3)+((1/252)*h^2+(23/28350)*h^2*u^2+(809/7484400)*h^2*u^4+(27827/2270268000)*h^2*u^6+(637171/490377888000)*h^2*u^8+(33500737/250092722880000)*h^2*u^10)*f(4):

#subroutine 3

inx:=0:
ind:=0:
iny:=1:
h:=Pi/4.0:
n:=0:
omega:=5:
u:=omega*h:
N:=solve(h*p = 500*Pi/2, p):

c:=1:
for j from 0 to 5 do
    t[j]:=inx+j*h:
end do:
#e||(1..6);
vars:=y[n+1],y[n+2],y[n+3],delta[n],y[n+4]:

printf("%6s%15s%15s%15s\n",
    "h","Num.y","Ex.y","Error y");
for k from 1 to N do

    par1:=x[0]=t[0],x[1]=t[1],x[2]=t[2],x[3]=t[3],x[4]=t[4],x[5]=t[5]:
    par2:=y[n]=iny,delta[n]=ind:
   

res:=eval(<vars>, fsolve(eval({e||(1..5)},[par1,par2]), {vars}));

    for i from 1 to 5 do
        exy:=eval(0.5*cos(5*c*h)+0.5*cos(c*h)):
        printf("%6.5f%17.9f%15.9f%13.5g\n",
        h*c,res[i],exy,abs(res[i]-exy)):
        
        c:=c+1:
    end do:
    iny:=res[5]:
    inx:=t[5]:
    for j from 0 to 5 do
        t[j]:=inx + j*h:
    end do:
end do:

i want to solve this DAE system usin Dsolve , but i obtain this error message (cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up), if anyone can help me ,

I'm studying for an exam and earlier today I was working in my Maple sheet. I saved it as usual and no .bak file was in the directory afterwards. When I now later in the day tried to open it, I got the pop up message:
"There were problems during the loading process. your worksheet may be incomplete" and half of the content is missing.

I've searched on google and tried to solve it myself, unfortunately without any luck.

I would really appreciate any help.

Best regards

Hi everybody,

I am used to using  the DocumentTools :-RunWorksheet command and I am confronted with the following problem :

• My worksheet is deemed to generate a plot in a png file
  > plotsetup(png, plotoutput=MyFile, …)
  > plot( …)
  But MyFile is not created
   
• Thinking that the mw file launched by  DocumentTools :-RunWorksheet is seen as a procedure, I have thought that print(plot(…)) would fix the issue.
  Unfortunately the png file is still not created (same behavior with a jpeg file)

I know that  DocumentTools :-RunWorksheet is “experimental” but I wonder if I am doing something wrong or if DocumentTools :-RunWorksheet simply does not support plots ?

Thanks in advance

proc:=changecoords([x,y],logrithmic);
dsolvediff(x,t):=Matrix([[ 1 , 0],
        [ 0 , i ]])x+Vector[column]([ x^i ,
                 0]);
x:=y+h(y);
for i from 2 to 10;
solve;
end do;

endproc;

     
MakeIteration := proc( expr::algebraic, x::name )
    local iteration := diff(x,t)=Matrix([[ 1 , 0 ],
        [ 0 , i]])x+Vector[column]([ x^i ,
                 0]),x:=y+h(y);
for i from 2 to 10 ;
end do ;
    unapply(iteration, x);
endproc;
Error, missing operator or `;`

Hi , I would like to solve nonlinear equation by using maple,but I wander how I can write it since there is a change of veriable bysubstiuting the value of y in the diifferenitat . Iactually coudnot write the equation sine it contains differential ,matrix and vector . do Ihave to use dalembertian? 

best regards 

Dear MaplePrimes team,

For display a beautiful parametric surface with hole (or pierced surface), unfortunately unlike CAD (computer-aided design) tool, Maple requires a large grid number. Therefore the computing is too long and requires huge RAM only with grid of [500,500] on a modern computer.

Fig. 1: For a complex surface such an aircraft fuselage here, Needs high grid, therefore, the compilation is too long with modern computer (Intel Core i7, 2.4 GHz CPU, 16 GB RAM). If displays supplementary windows holes on fuselage, the software may bug when the RAM is full.

Question 1:

In matter of low cost computation, do you have better solution to create a fast surface with smooth hole from given a parametric surface equation S(x,y) and given any convex/concave-closed parametric curve C(t) that is projected on surface S(x,y)?

Fig. 2: These surfaces are been created in Maple 2016 from given initial parametric surface equation and curve projected on the surface. But requires huge grid, huge RAM, and long time to get smooth hole when free CAD tools are fast and low RAM.

Question 2:

Because I noted that the Maple’s view option renderers smooth edges of any surface. My question is: Is it possible to use the internal structure of display/view used by Maple to apply at free boundaries? I think it will be possible to create many class of view, for examples: cylindrical sector, spherical sector views or more rather to be limited with conventional cubic view. And thus, I think it will be possible to create own smooth hole or multiple-hole on surface and get smooth pierced surface.

I know that almost of technicians/engineers will recommend me to use a CAD tool to create surface with hole. But the objective here is to keep purely a mathematical mind and work with exact equations (analytic equations).

On a free CAD tool, even the complex holes are created very fast only with low RAM. Why not on Maple?

Best.

Guy.

Hi, is anyone using the Geometry Expressions software together with Maple? I've found about this software on forum and installed a free demo version. It is using symbolic geometry, which I haven't been able to find this feature on other software, and can work very well with Maple, but unfortunatelly, my demo version doesn't work properly, and their oficial website http://saltire.com/ has lots of errors 404 page not found. I have requested support, but have had no answer so far. I was so happy finding this software, but now I am thinking maybe wasting my time. If you are using it, or maybe think it would be good to give it a go, please let me know if it is working for you. A particular feature which is not working for me is 'creating angles'. Thank you.

Dears I have the following statment in Matlab

r=8;             ZUM=U(1)-YU(1);            IT=0;

for r=2:10

    ZU(r)=abs(U(r)-YU(r));

    if ZU(r)> ZUM

        ZUM=ZU(r);

    else

        ZUM=ZUM;

    end

end

ZUM;

while IT < 20

    IT=IT+1

    if ZUM < (0.1)^r

    IT=20;

    else

  for r=1:Nx

  YU(r)=U(r);

  end

YU;

I need to write this statment in Maple

Please I need Correction on this code particularly if I can make do without the declaration of vector in the third subroutine . The idea is to get maximum error. The code has 3 subroutine. The problem I think is in the third subroutine (Display of results).

Thank you in anticipation of positive response.

# First Declaration of the problem

restart:
Digits:=30:
interface(rtablesize=infinity):

f1:=proc(n)
    y2[n]:
end proc:
f2:=proc(n)
    -y1[n]+0.001*cos(t[n]):
end proc:
f3:=proc(n)
    y4[n]:
end proc:
f4:=proc(n)
    -y3[n]+0.001*sin(t[n]):
end proc:
F1:=proc(n)
    f2(n):
end proc:
F2:=proc(n)
    -(f1(n))-0.001*sin(t[n]):
end proc:
F3:=proc(n)
    f4(n):
end proc:
F4:=proc(n)
    -f3(n)+0.001*cos(t[n]):
end proc:

# Declaration of the Numerical methods

e1:=y1[n+2] = (7/23)*y1[n]+(16/23)*y1[n+1]+(12/23)*f1(n+2)*h+(16/23)*f1(n+1)*h-(2/23)*F1(n+2)*h^2+(2/23)*h*f1(n)+((24/3703)*y1[n]-(24/3703)*y1[n+1]+(48/18515)*f1(n+2)*h+(8/55545)*f1(n+1)*h-(116/55545)*F1(n+2)*h^2+(208/55545)*h*f1(n))*u^2+((901/2980915)*y1[n]-(901/2980915)*y1[n+1]+(7109/89427450)*f1(n+2)*h+(923/14904575)*f1(n+1)*h-(6241/89427450)*F1(n+2)*h^2+(14383/89427450)*h*f1(n))*u^4+((1979723/158376013950)*y1[n]-(1979723/158376013950)*y1[n+1]+(6364571/2375640209250)*f1(n+2)*h+(728327/215967291750)*f1(n+1)*h-(11785633/4751280418500)*F1(n+2)*h^2+(5106559/791880069750)*h*f1(n))*u^6+((6488435581/13259239887894000)*y1[n]-(6488435581/13259239887894000)*y1[n+1]+(8693517709/91794737685420000)*f1(n+2)*h+(260601208141/1789997384865690000)*f1(n+1)*h-(323357994149/3579994769731380000)*F1(n+2)*h^2+(891627999937/3579994769731380000)*h*f1(n))*u^8+((25090513463/1343541160668420000)*y1[n]-(25090513463/1343541160668420000)*y1[n+1]+(190450718149/55421072877572325000)*f1(n+2)*h+(47563947061/8210529315195900000)*f1(n+1)*h-(1475729910283/443368583020578600000)*F1(n+2)*h^2+(261738159769/27710536438786162500)*h*f1(n))*u^10+((244426606265778733/347060946154014557665200000)*y1[n]-(244426606265778733/347060946154014557665200000)*y1[n+1]+(1316372988977975777/10411828384620436729956000000)*f1(n+2)*h+(105391490263288387/473264926573656214998000000)*f1(n+1)*h-(1284959669761615073/10411828384620436729956000000)*F1(n+2)*h^2+(72506125749079249/204153497737655622156000000)*h*f1(n))*u^12:

e2:=h^2*F1(n+1) = (60/23)*y1[n]-(60/23)*y1[n+1]+(25/46)*f1(n+2)*h+(32/23)*f1(n+1)*h-(4/23)*F1(n+2)*h^2+(31/46)*h*f1(n)+((209/3703)*y1[n]-(209/3703)*y1[n+1]+(1313/222180)*f1(n+2)*h+(1304/55545)*f1(n+1)*h-(131/18515)*F1(n+2)*h^2+(6011/222180)*h*f1(n))*u^2+((77491/35770980)*y1[n]-(77491/35770980)*y1[n+1]+(574843/2146258800)*f1(n+2)*h+(113536/134141175)*f1(n+1)*h-(53461/178854900)*F1(n+2)*h^2+(2258041/2146258800)*h*f1(n))*u^4+((151508243/1900512167400)*y1[n]-(151508243/1900512167400)*y1[n+1]+(1290306599/114030730044000)*f1(n+2)*h+(18919693/647901875250)*f1(n+1)*h-(113769323/9502560837000)*F1(n+2)*h^2+(4470322013/114030730044000)*h*f1(n))*u^6+((42120775181/14464625332248000)*y1[n]-(42120775181/14464625332248000)*y1[n+1]+(332746636891/734357901483360000)*f1(n+2)*h+(302396120633/298332897477615000)*f1(n+1)*h-(369019384141/795554393273640000)*F1(n+2)*h^2+(13797329479621/9546652719283680000)*h*f1(n))*u^8+((18953368786273/177347433208231440000)*y1[n]-(18953368786273/177347433208231440000)*y1[n+1]+(2430202319484337/138330997902420523200000)*f1(n+2)*h+(310803544671199/8645687368901282700000)*f1(n+1)*h-(203453960588449/11527583158535043600000)*F1(n+2)*h^2+(7380568619069419/138330997902420523200000)*h*f1(n))*u^10+((16436168060905785763/4164731353848174691982400000)*y1[n]-(16436168060905785763/4164731353848174691982400000)*y1[n+1]+(167160345356705269819/249883881230890481518944000000)*f1(n+2)*h+(461636091223370027/354948694930242161248500000)*f1(n+1)*h-(13852288092290788813/20823656769240873459912000000)*F1(n+2)*h^2+(29059878239787610409/14699051837111204795232000000)*h*f1(n))*u^12:

e3:=y2[n+2] = (7/23)*y2[n]+(16/23)*y2[n+1]+(12/23)*f2(n+2)*h+(16/23)*f2(n+1)*h-(2/23)*F2(n+2)*h^2+(2/23)*h*f2(n)+((24/3703)*y2[n]-(24/3703)*y2[n+1]+(48/18515)*f2(n+2)*h+(8/55545)*f2(n+1)*h-(116/55545)*F2(n+2)*h^2+(208/55545)*h*f2(n))*u^2+((901/2980915)*y2[n]-(901/2980915)*y2[n+1]+(7109/89427450)*f2(n+2)*h+(923/14904575)*f2(n+1)*h-(6241/89427450)*F2(n+2)*h^2+(14383/89427450)*h*f2(n))*u^4+((1979723/158376013950)*y2[n]-(1979723/158376013950)*y2[n+1]+(6364571/2375640209250)*f2(n+2)*h+(728327/215967291750)*f2(n+1)*h-(11785633/4751280418500)*F2(n+2)*h^2+(5106559/791880069750)*h*f2(n))*u^6+((6488435581/13259239887894000)*y2[n]-(6488435581/13259239887894000)*y2[n+1]+(8693517709/91794737685420000)*f2(n+2)*h+(260601208141/1789997384865690000)*f2(n+1)*h-(323357994149/3579994769731380000)*F2(n+2)*h^2+(891627999937/3579994769731380000)*h*f2(n))*u^8+((25090513463/1343541160668420000)*y2[n]-(25090513463/1343541160668420000)*y2[n+1]+(190450718149/55421072877572325000)*f2(n+2)*h+(47563947061/8210529315195900000)*f2(n+1)*h-(1475729910283/443368583020578600000)*F2(n+2)*h^2+(261738159769/27710536438786162500)*h*f2(n))*u^10+((244426606265778733/347060946154014557665200000)*y2[n]-(244426606265778733/347060946154014557665200000)*y2[n+1]+(1316372988977975777/10411828384620436729956000000)*f2(n+2)*h+(105391490263288387/473264926573656214998000000)*f2(n+1)*h-(1284959669761615073/10411828384620436729956000000)*F2(n+2)*h^2+(72506125749079249/204153497737655622156000000)*h*f2(n))*u^12:

e4:=h^2*F2(n+1) = (60/23)*y2[n]-(60/23)*y2[n+1]+(25/46)*f2(n+2)*h+(32/23)*f2(n+1)*h-(4/23)*F2(n+2)*h^2+(31/46)*h*f2(n)+((209/3703)*y2[n]-(209/3703)*y2[n+1]+(1313/222180)*f2(n+2)*h+(1304/55545)*f2(n+1)*h-(131/18515)*F2(n+2)*h^2+(6011/222180)*h*f2(n))*u^2+((77491/35770980)*y2[n]-(77491/35770980)*y2[n+1]+(574843/2146258800)*f2(n+2)*h+(113536/134141175)*f2(n+1)*h-(53461/178854900)*F2(n+2)*h^2+(2258041/2146258800)*h*f2(n))*u^4+((151508243/1900512167400)*y2[n]-(151508243/1900512167400)*y2[n+1]+(1290306599/114030730044000)*f2(n+2)*h+(18919693/647901875250)*f2(n+1)*h-(113769323/9502560837000)*F2(n+2)*h^2+(4470322013/114030730044000)*h*f2(n))*u^6+((42120775181/14464625332248000)*y2[n]-(42120775181/14464625332248000)*y2[n+1]+(332746636891/734357901483360000)*f2(n+2)*h+(302396120633/298332897477615000)*f2(n+1)*h-(369019384141/795554393273640000)*F2(n+2)*h^2+(13797329479621/9546652719283680000)*h*f2(n))*u^8+((18953368786273/177347433208231440000)*y2[n]-(18953368786273/177347433208231440000)*y2[n+1]+(2430202319484337/138330997902420523200000)*f2(n+2)*h+(310803544671199/8645687368901282700000)*f2(n+1)*h-(203453960588449/11527583158535043600000)*F2(n+2)*h^2+(7380568619069419/138330997902420523200000)*h*f2(n))*u^10+((16436168060905785763/4164731353848174691982400000)*y2[n]-(16436168060905785763/4164731353848174691982400000)*y2[n+1]+(167160345356705269819/249883881230890481518944000000)*f2(n+2)*h+(461636091223370027/354948694930242161248500000)*f2(n+1)*h-(13852288092290788813/20823656769240873459912000000)*F2(n+2)*h^2+(29059878239787610409/14699051837111204795232000000)*h*f2(n))*u^12:

e5:=y3[n+2] = (7/23)*y3[n]+(16/23)*y3[n+1]+(12/23)*f3(n+2)*h+(16/23)*f3(n+1)*h-(2/23)*F3(n+2)*h^2+(2/23)*h*f3(n)+((24/3703)*y3[n]-(24/3703)*y3[n+1]+(48/18515)*f3(n+2)*h+(8/55545)*f3(n+1)*h-(116/55545)*F3(n+2)*h^2+(208/55545)*h*f3(n))*u^2+((901/2980915)*y3[n]-(901/2980915)*y3[n+1]+(7109/89427450)*f3(n+2)*h+(923/14904575)*f3(n+1)*h-(6241/89427450)*F3(n+2)*h^2+(14383/89427450)*h*f3(n))*u^4+((1979723/158376013950)*y3[n]-(1979723/158376013950)*y3[n+1]+(6364571/2375640209250)*f3(n+2)*h+(728327/215967291750)*f3(n+1)*h-(11785633/4751280418500)*F3(n+2)*h^2+(5106559/791880069750)*h*f3(n))*u^6+((6488435581/13259239887894000)*y3[n]-(6488435581/13259239887894000)*y3[n+1]+(8693517709/91794737685420000)*f3(n+2)*h+(260601208141/1789997384865690000)*f3(n+1)*h-(323357994149/3579994769731380000)*F3(n+2)*h^2+(891627999937/3579994769731380000)*h*f3(n))*u^8+((25090513463/1343541160668420000)*y3[n]-(25090513463/1343541160668420000)*y3[n+1]+(190450718149/55421072877572325000)*f3(n+2)*h+(47563947061/8210529315195900000)*f3(n+1)*h-(1475729910283/443368583020578600000)*F3(n+2)*h^2+(261738159769/27710536438786162500)*h*f3(n))*u^10+((244426606265778733/347060946154014557665200000)*y3[n]-(244426606265778733/347060946154014557665200000)*y3[n+1]+(1316372988977975777/10411828384620436729956000000)*f3(n+2)*h+(105391490263288387/473264926573656214998000000)*f3(n+1)*h-(1284959669761615073/10411828384620436729956000000)*F3(n+2)*h^2+(72506125749079249/204153497737655622156000000)*h*f3(n))*u^12:
e6:=h^2*F3(n+1) = (60/23)*y3[n]-(60/23)*y3[n+1]+(25/46)*f3(n+2)*h+(32/23)*f3(n+1)*h-(4/23)*F3(n+2)*h^2+(31/46)*h*f3(n)+((209/3703)*y3[n]-(209/3703)*y3[n+1]+(1313/222180)*f3(n+2)*h+(1304/55545)*f3(n+1)*h-(131/18515)*F3(n+2)*h^2+(6011/222180)*h*f3(n))*u^2+((77491/35770980)*y3[n]-(77491/35770980)*y3[n+1]+(574843/2146258800)*f3(n+2)*h+(113536/134141175)*f3(n+1)*h-(53461/178854900)*F3(n+2)*h^2+(2258041/2146258800)*h*f3(n))*u^4+((151508243/1900512167400)*y3[n]-(151508243/1900512167400)*y3[n+1]+(1290306599/114030730044000)*f3(n+2)*h+(18919693/647901875250)*f3(n+1)*h-(113769323/9502560837000)*F3(n+2)*h^2+(4470322013/114030730044000)*h*f3(n))*u^6+((42120775181/14464625332248000)*y3[n]-(42120775181/14464625332248000)*y3[n+1]+(332746636891/734357901483360000)*f3(n+2)*h+(302396120633/298332897477615000)*f3(n+1)*h-(369019384141/795554393273640000)*F3(n+2)*h^2+(13797329479621/9546652719283680000)*h*f3(n))*u^8+((18953368786273/177347433208231440000)*y3[n]-(18953368786273/177347433208231440000)*y3[n+1]+(2430202319484337/138330997902420523200000)*f3(n+2)*h+(310803544671199/8645687368901282700000)*f3(n+1)*h-(203453960588449/11527583158535043600000)*F3(n+2)*h^2+(7380568619069419/138330997902420523200000)*h*f3(n))*u^10+((16436168060905785763/4164731353848174691982400000)*y3[n]-(16436168060905785763/4164731353848174691982400000)*y3[n+1]+(167160345356705269819/249883881230890481518944000000)*f3(n+2)*h+(461636091223370027/354948694930242161248500000)*f3(n+1)*h-(13852288092290788813/20823656769240873459912000000)*F3(n+2)*h^2+(29059878239787610409/14699051837111204795232000000)*h*f3(n))*u^12:

e7:=y4[n+2] = (7/23)*y4[n]+(16/23)*y4[n+1]+(12/23)*f4(n+2)*h+(16/23)*f4(n+1)*h-(2/23)*F4(n+2)*h^2+(2/23)*h*f4(n)+((24/3703)*y4[n]-(24/3703)*y4[n+1]+(48/18515)*f4(n+2)*h+(8/55545)*f4(n+1)*h-(116/55545)*F4(n+2)*h^2+(208/55545)*h*f4(n))*u^2+((901/2980915)*y4[n]-(901/2980915)*y4[n+1]+(7109/89427450)*f4(n+2)*h+(923/14904575)*f4(n+1)*h-(6241/89427450)*F4(n+2)*h^2+(14383/89427450)*h*f4(n))*u^4+((1979723/158376013950)*y4[n]-(1979723/158376013950)*y4[n+1]+(6364571/2375640209250)*f4(n+2)*h+(728327/215967291750)*f4(n+1)*h-(11785633/4751280418500)*F4(n+2)*h^2+(5106559/791880069750)*h*f4(n))*u^6+((6488435581/13259239887894000)*y4[n]-(6488435581/13259239887894000)*y4[n+1]+(8693517709/91794737685420000)*f4(n+2)*h+(260601208141/1789997384865690000)*f4(n+1)*h-(323357994149/3579994769731380000)*F4(n+2)*h^2+(891627999937/3579994769731380000)*h*f4(n))*u^8+((25090513463/1343541160668420000)*y4[n]-(25090513463/1343541160668420000)*y4[n+1]+(190450718149/55421072877572325000)*f4(n+2)*h+(47563947061/8210529315195900000)*f4(n+1)*h-(1475729910283/443368583020578600000)*F4(n+2)*h^2+(261738159769/27710536438786162500)*h*f4(n))*u^10+((244426606265778733/347060946154014557665200000)*y4[n]-(244426606265778733/347060946154014557665200000)*y4[n+1]+(1316372988977975777/10411828384620436729956000000)*f4(n+2)*h+(105391490263288387/473264926573656214998000000)*f4(n+1)*h-(1284959669761615073/10411828384620436729956000000)*F4(n+2)*h^2+(72506125749079249/204153497737655622156000000)*h*f4(n))*u^12:

e8:=h^2*F4(n+1) = (60/23)*y4[n]-(60/23)*y4[n+1]+(25/46)*f4(n+2)*h+(32/23)*f4(n+1)*h-(4/23)*F4(n+2)*h^2+(31/46)*h*f4(n)+((209/3703)*y4[n]-(209/3703)*y4[n+1]+(1313/222180)*f4(n+2)*h+(1304/55545)*f4(n+1)*h-(131/18515)*F4(n+2)*h^2+(6011/222180)*h*f4(n))*u^2+((77491/35770980)*y4[n]-(77491/35770980)*y4[n+1]+(574843/2146258800)*f4(n+2)*h+(113536/134141175)*f4(n+1)*h-(53461/178854900)*F4(n+2)*h^2+(2258041/2146258800)*h*f4(n))*u^4+((151508243/1900512167400)*y4[n]-(151508243/1900512167400)*y4[n+1]+(1290306599/114030730044000)*f4(n+2)*h+(18919693/647901875250)*f4(n+1)*h-(113769323/9502560837000)*F4(n+2)*h^2+(4470322013/114030730044000)*h*f4(n))*u^6+((42120775181/14464625332248000)*y4[n]-(42120775181/14464625332248000)*y4[n+1]+(332746636891/734357901483360000)*f4(n+2)*h+(302396120633/298332897477615000)*f4(n+1)*h-(369019384141/795554393273640000)*F4(n+2)*h^2+(13797329479621/9546652719283680000)*h*f4(n))*u^8+((18953368786273/177347433208231440000)*y4[n]-(18953368786273/177347433208231440000)*y4[n+1]+(2430202319484337/138330997902420523200000)*f4(n+2)*h+(310803544671199/8645687368901282700000)*f4(n+1)*h-(203453960588449/11527583158535043600000)*F4(n+2)*h^2+(7380568619069419/138330997902420523200000)*h*f4(n))*u^10+((16436168060905785763/4164731353848174691982400000)*y4[n]-(16436168060905785763/4164731353848174691982400000)*y4[n+1]+(167160345356705269819/249883881230890481518944000000)*f4(n+2)*h+(461636091223370027/354948694930242161248500000)*f4(n+1)*h-(13852288092290788813/20823656769240873459912000000)*F4(n+2)*h^2+(29059878239787610409/14699051837111204795232000000)*h*f4(n))*u^12:

# Display of the solutions

h:=evalf(Pi/6):

omega:=1.0:
u:=omega*h:
N:=solve(h*p = 12*Pi/6, p):
n:=0:

exy1:= [seq](eval(cos(i)+0.0005*i*sin(i)), i=h..N,h):
exy2:= [seq](eval(-0.9995*sin(i)+0.0005), i=h..N,h):
exy3:= [seq](eval(sin(i)-0.0005*i*cos(i)), i=h..N,h):
exy4:= [seq](eval(0.9995*sin(i)+0.0005*i*sin(i)), i=h..N,h):

iny1:=1:
iny2:=0:
iny3:=0:
iny4:=0.9995:

err1 := Vector(N):
err2 := Vector(N):
c:=1:
inx:=0:
vars := y1[n+1],y1[n+2],y2[n+1],y2[n+2],y3[n+1],y3[n+2],y4[n+1],y4[n+2]:
for j from 0 to 2 do
    x[j]:=inx+j*h:
end do:
printf("%4s%9s%9s%9s%9s%9s%9s%10s%10s%9s%9s%9s%10s\n",
    "h","numy1","numy2","numy3","numy4",
    "exy1","exy2","exy3","exy4",
    "erry1","erry2","erry3","erry4");
    
st := time():
for k from 1 to N/2 do
    param1:=y1[n]=iny1,y2[n]=iny2,y3[n]=iny3,y4[n]=iny4:
    param2:=t[n]=x[0],t[n+1]=x[1],t[n+2]=x[2]:
    
    res:=eval(<vars>, fsolve(eval({e||(1..8)},[param1,param2]),{vars})):
    
    for i from 1 to 2 do
        printf("%5.2f%9.3f%9.3f%9.3f%9.3f %8.5f%10.5f%10.5f%10.5f %8.2g%9.3g%9.3g%8.3g\n",
        h*c,res[i],res[i+2],res[i+4],res[i+6],
        exy1[c],exy2[c],exy3[c],exy4[c],
        abs(res[i]-exy1[c]),abs(res[i+2]-exy2[c]),abs(res[i+4]-exy3[c]),abs(res[i+6]-exy4[c])):

        err1[c] := abs(evalf(res[i]-exy1)):
        err2[c] := abs(evalf(res[i+4]-exy3)):
        c:=c+1:
    end do:
    iny1:=res[2]:
    iny2:=res[4]:
    iny3:=res[6]:
    iny4:=res[8]:
    inx:=x[2]:
    for j from 0 to 2 do
        x[j]:=inx+j*h:
    end do:
end do:
v:=time() - st;
printf("Maximum error is %.13g", max(err1));
printf("Maximum error is %.13g", max(err2));

i tried to solve a nonlinear ode with numerical method but maple can't solve it and this error occur:

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

my maple codes are attached below:

numeriacal_sol.mw

can any help me?

hi--how i can solve following equation?

thanks

Eq.mw


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