Dearz

Hope you would be fine with everything. I try to solve the following linear system of equations via fsolve command but the solution doesn't satisfied the system please see and put your valueable comments. Waiting your positive response.

-5.7167551941125971285 d[1, 1] - 0.23520507704562101132 d[1, 2]

   - 4.7759348859301130832 d[1, 3]

   + 82.882747548740738074 d[1, 4]

   + 1.5473302855836067493 d[2, 1]

   + 0.063661977236758134308 d[2, 2]

   + 1.2926823766365742120 d[2, 3]

   - 22.433527600870893213 d[2, 4]

   - 11.906076336447024126 d[3, 1]

   - 0.48985298599265354856 d[3, 2]

   - 9.9466643924764099316 d[3, 3]

   + 172.61685795222431091 d[3, 4]

   + 153.42462622364681378 d[4, 1]

   - 17.156128463674125233 d[4, 2]

   + 222.04914007834331471 d[4, 3]

   - 2162.1913920527683546 d[4, 4] = 0
-6.3505370802317673052 d[1, 1] - 0.23520507704562101132 d[1, 2]

   - 5.4097167720492832599 d[1, 3]

   + 54.802782951629695640 d[1, 4]

   + 1.7188733853924696263 d[2, 1]

   + 0.063661977236758134308 d[2, 2]

   + 1.4642254764454370890 d[2, 3]

   - 14.833240696164645293 d[2, 4]

   - 13.226030621801645811 d[3, 1]

   - 0.48985298599265354856 d[3, 2]

   - 11.266618677831031617 d[3, 3]

   + 114.13574573628827681 d[3, 4]

   + 107.19584752215150208 d[4, 1]

   - 17.156128463674125233 d[4, 2]

   + 175.82036137684800302 d[4, 3]

   - 1136.3239123361047712 d[4, 4] = 0
-6.7642088272251297212 d[1, 1] - 0.23520507704562101132 d[1, 2]

   - 5.8233885190426456759 d[1, 3]

   + 34.632657184619275137 d[1, 4]

   + 1.8308401918550417305 d[2, 1]

   + 0.063661977236758134308 d[2, 2]

   + 1.5761922829080091932 d[2, 3] - 9.373876878125528749 d[2, 4]

   - 14.087569594645296643 d[3, 1]

   - 0.48985298599265354856 d[3, 2]

   - 12.128157650674682449 d[3, 3]

   + 72.128164697121390121 d[3, 4]

   + 77.022155175221117487 d[4, 1]

   - 17.156128463674125233 d[4, 2]

   + 145.64666902991761843 d[4, 3]

   - 601.11088029977885095 d[4, 4] = 0
-1.5473302855836067487 d[1, 1] - 0.06366197723675813430 d[1, 2]

   - 1.2926823766365742115 d[1, 3]

   + 22.433527600870893218 d[1, 4]

   + 1.5473302855836067493 d[2, 1]

   + 0.063661977236758134308 d[2, 2]

   + 1.2926823766365742120 d[2, 3]

   - 22.433527600870893213 d[2, 4]

   - 7.7366514279180337465 d[3, 1]

   - 0.31830988618379067154 d[3, 2]

   - 6.4634118831828710599 d[3, 3]

   + 112.16763800435446606 d[3, 4]

   + 104.66490008068725185 d[4, 1]

   - 19.162255148264198426 d[4, 2]

   + 181.31392067374404557 d[4, 3]

   - 1455.2623850848598494 d[4, 4] = 0
-1.7188733853924696257 d[1, 1] - 0.06366197723675813430 d[1, 2]

   - 1.4642254764454370885 d[1, 3]

   + 14.833240696164645297 d[1, 4]

   + 1.7188733853924696263 d[2, 1]

   + 0.063661977236758134308 d[2, 2]

   + 1.4642254764454370890 d[2, 3]

   - 14.833240696164645293 d[2, 4]

   - 8.5943669269623481316 d[3, 1]

   - 0.31830988618379067154 d[3, 2]

   - 7.3211273822271854450 d[3, 3]

   + 74.166203480823226458 d[3, 4]

   + 53.030427038219525869 d[4, 1]

   - 19.162255148264198426 d[4, 2]

   + 129.67944763127631958 d[4, 3]

   - 668.89639482661771723 d[4, 4] = 0
-1.8308401918550417299 d[1, 1] - 0.06366197723675813430 d[1, 2]

   - 1.5761922829080091926 d[1, 3] + 9.373876878125528754 d[1, 4]

   + 1.8308401918550417305 d[2, 1]

   + 0.063661977236758134308 d[2, 2]

   + 1.5761922829080091932 d[2, 3] - 9.373876878125528749 d[2, 4]

   - 9.1542009592752086523 d[3, 1]

   - 0.31830988618379067154 d[3, 2]

   - 7.8809614145400459657 d[3, 3]

   + 46.869384390627643742 d[3, 4]

   + 19.328418292985322519 d[4, 1]

   - 19.162255148264198426 d[4, 2]

   + 95.977438886042116228 d[4, 3]

   - 305.71973224709969080 d[4, 4] = 0
 7.0561523113686303394 d[1, 1] - 1.9098593171027440292 d[1, 2]

    + 14.695589579779606456 d[1, 3]

    - 96.471127562654332340 d[1, 4]

    - 2.3520507704562101132 d[2, 1]

    + 0.63661977236758134308 d[2, 2]

    - 4.8985298599265354856 d[2, 3]

    + 32.157042520884777447 d[2, 4]

    + 16.464355393193470792 d[3, 1]

    - 4.4563384065730694016 d[3, 2]

    + 34.289709019485748399 d[3, 3]

    - 225.09929764619344213 d[3, 4]

    - 96.434081588704614639 d[4, 1]

    + 26.101410667070835066 d[4, 2]

    - 200.83972425698795490 d[4, 3]

    + 1318.4387433562758754 d[4, 4] = 0
-2.3520507704562101132 d[1, 1] + 0.6366197723675813431 d[1, 2]

   - 4.898529859926535486 d[1, 3] + 32.157042520884777450 d[1, 4]

   - 2.3520507704562101132 d[2, 1]

   + 0.63661977236758134308 d[2, 2]

   - 4.8985298599265354856 d[2, 3]

   + 32.157042520884777447 d[2, 4]

   + 7.0561523113686303394 d[3, 1]

   - 1.9098593171027440293 d[3, 2]

   + 14.695589579779606457 d[3, 3] - 96.47112756265433234 d[3, 4]

   - 11.760253852281050559 d[4, 1] + 3.183098861837906715 d[4, 2]

   - 24.49264929963267742 d[4, 3] + 160.7852126044238874 d[4, 4] = 

  1
1.9098593171027440291 d[1, 1] - 1.9098593171027440292 d[1, 2]

   + 9.5492965855137201456 d[1, 3]

   - 36.287327024952136554 d[1, 4]

   - 0.6366197723675813430 d[2, 1]

   + 0.63661977236758134308 d[2, 2]

   - 3.1830988618379067154 d[2, 3]

   + 12.095775674984045518 d[2, 4]

   + 4.4563384065730694010 d[3, 1]

   - 4.4563384065730694016 d[3, 2]

   + 22.281692032865347008 d[3, 3] - 84.67042972488831863 d[3, 4]

   - 26.101410667070835067 d[4, 1]

   + 26.101410667070835066 d[4, 2]

   - 130.50705333535417533 d[4, 3]

   + 495.92680267434586630 d[4, 4] = 0
-0.6366197723675813431 d[1, 1] + 0.6366197723675813431 d[1, 2]

   - 3.1830988618379067164 d[1, 3]

   + 12.095775674984045516 d[1, 4]

   - 0.6366197723675813430 d[2, 1]

   + 0.63661977236758134308 d[2, 2]

   - 3.1830988618379067154 d[2, 3]

   + 12.095775674984045518 d[2, 4]

   + 1.9098593171027440288 d[3, 1]

   - 1.9098593171027440293 d[3, 2] + 9.549296585513720146 d[3, 3]

   - 36.287327024952136560 d[3, 4] - 3.183098861837906717 d[4, 1]

   + 3.183098861837906715 d[4, 2] - 15.91549430918953358 d[4, 3]

   + 60.47887837492022764 d[4, 4] = 1
-1.4491448767744190950 d[1, 1] - 1.9098593171027440292 d[1, 2]

   + 6.1902923916365570215 d[1, 3]

   - 11.964006709004497915 d[1, 4]

   + 0.4830482922581396984 d[2, 1]

   + 0.63661977236758134308 d[2, 2]

   - 2.0634307972121856740 d[2, 3] + 3.988002236334832639 d[2, 4]

   - 3.381338045806977889 d[3, 1] - 4.4563384065730694016 d[3, 2]

   + 14.444015580485299718 d[3, 3] - 27.91601565434382847 d[3, 4]

   + 19.804979982583727629 d[4, 1]

   + 26.101410667070835066 d[4, 2]

   - 84.600662685699612634 d[4, 3] + 163.5080916897281382 d[4, 4] = 

  0
0.4830482922581396984 d[1, 1] + 0.6366197723675813431 d[1, 2]

   - 2.0634307972121856744 d[1, 3] + 3.988002236334832645 d[1, 4]

   + 0.4830482922581396984 d[2, 1]

   + 0.63661977236758134308 d[2, 2]

   - 2.0634307972121856740 d[2, 3] + 3.988002236334832639 d[2, 4]

   - 1.4491448767744190956 d[3, 1]

   - 1.9098593171027440293 d[3, 2]

   + 6.1902923916365570221 d[3, 3] - 11.96400670900449791 d[3, 4]

   + 2.415241461290698491 d[4, 1] + 3.183098861837906715 d[4, 2]

   - 10.317153986060928369 d[4, 3] + 19.94001118167416332 d[4, 4] = 

  1
 11.581726419330485018 d[1, 1] - 3.8605754731101616728 d[1, 2]

    + 27.024028311771131709 d[1, 3]

    - 158.28359439751662858 d[1, 4]

    - 1.9098593171027440292 d[2, 1]

    + 0.63661977236758134308 d[2, 2]

    - 4.4563384065730694016 d[2, 3]

    + 26.101410667070835066 d[2, 4]

    + 19.221163687741461135 d[3, 1]

    - 6.4070545625804870452 d[3, 2]

    + 44.849381938063409316 d[3, 3]

    - 262.68923706579996884 d[3, 4]

    - 172.31418534244454203 d[4, 1]

    + 57.438061780814847345 d[4, 2]

    - 402.06643246570393142 d[4, 3]

    + 2354.9605330134087411 d[4, 4] = 0
 7.0561523113686303394 d[1, 1] - 2.3520507704562101132 d[1, 2]

    + 16.464355393193470792 d[1, 3]

    - 96.434081588704614639 d[1, 4]

    - 1.9098593171027440292 d[2, 1]

    + 0.63661977236758134308 d[2, 2]

    - 4.4563384065730694016 d[2, 3]

    + 26.101410667070835066 d[2, 4]

    + 14.695589579779606456 d[3, 1]

    - 4.8985298599265354856 d[3, 2]

    + 34.289709019485748399 d[3, 3]

    - 200.83972425698795490 d[3, 4]

    - 96.471127562654332340 d[4, 1]

    + 32.157042520884777447 d[4, 2]

    - 225.09929764619344213 d[4, 3]

    + 1318.4387433562758753 d[4, 4] = 0
 1.9098593171027440291 d[1, 1] - 0.6366197723675813430 d[1, 2]

    + 4.4563384065730694010 d[1, 3]

    - 26.101410667070835067 d[1, 4]

    - 1.9098593171027440292 d[2, 1]

    + 0.63661977236758134308 d[2, 2]

    - 4.4563384065730694016 d[2, 3]

    + 26.101410667070835066 d[2, 4]

    + 9.5492965855137201456 d[3, 1]

    - 3.1830988618379067154 d[3, 2]

    + 22.281692032865347008 d[3, 3]

    - 130.50705333535417533 d[3, 4]

    - 36.287327024952136554 d[4, 1]

    + 12.095775674984045518 d[4, 2]

    - 84.670429724888318626 d[4, 3]

    + 495.92680267434586626 d[4, 4] = 0
-1.4491448767744190950 d[1, 1] + 0.4830482922581396984 d[1, 2]

   - 3.381338045806977889 d[1, 3] + 19.804979982583727629 d[1, 4]

   - 1.9098593171027440292 d[2, 1]

   + 0.63661977236758134308 d[2, 2]

   - 4.4563384065730694016 d[2, 3]

   + 26.101410667070835066 d[2, 4]

   + 6.1902923916365570215 d[3, 1]

   - 2.0634307972121856740 d[3, 2]

   + 14.444015580485299718 d[3, 3]

   - 84.600662685699612634 d[3, 4]

   - 11.964006709004497917 d[4, 1] + 3.988002236334832638 d[4, 2]

   - 27.91601565434382847 d[4, 3] + 163.50809168972813819 d[4, 4] = 

  0
Sols := solve([seq(`$`(F1[l1, l2], l1 = 2 .. 2^K*M-1), l2 = 2 .. 2^K*M), seq(`$`(F2[l1], l1 = 2 .. 2^K*M)), seq(`$`(F3[l1], l1 = 2 .. 2^K*M)), seq(`$`(F4[l1], l1 = 1 .. 2^K*M))], {seq(`$`(d[l1, l2], l1 = 1 .. 2^K*M), l2 = 1 .. 2^K*M)});
map(evalf, subs(Sols, convert(F4, list)));

 

Dearz!

Hope everyone is fine with everything. I am facing problem to solve the system of PDEs in the attached file. Is there any built-in command to the solve the attached system of PDEs via FEM, FDM, SIMPLER algorithm or some other efficient method? Please try to fix my problem. I am waiting your positive response. Thanks in advance.

PDEs_sol.mw

problem.mw
 

>  >  >  >  >  >  (1) (2) >  (3) >  Error, invalid input: norm expects its 1st argument, p, to be of type {Matrix, Vector, matrix, polynom, vector}, but received 92.359325848696162368355511315798*x^4+7.1870894227877814492593273580981*x^2-0.68000000000000000000000000000000e-31*x-34.149715256645549592146037526614*x^3-135.58601962203264776595890928687*x^5+101.25962748430115463423633295054*x^6-30.114080251339988529197699897019*x^7-x^1.25   >

 

Download problem.mw

 

Hello,

Could you please help me with the following problem? I'm new to Maple and i need some help.

Solve the equation x^3 - a*x + 1 = 0 , in x. Determine the particular solution for a=1,2,... .Graphically represent the polynom that appears in the equation, in a case where the equation has a real root and in a case where the equation has 3 real roots.

Thank you !

Hi everibody 

I work with Maple 2015 under OS-X El Capitan.

Using more than one matrix vector product (either M.V  or MatrixVectorMultiply(M,V)  ; M is a n by p matrix and V a column vector of size p) within the same block of commands generates an error.

Do other people have the same problem ?
Thanks for your feedback.

SomethingGoesWrong.mw


PS : I know I can do this   X . <<1, 1, -1> | <-1, 2, 0>> but this doesn't explain the error I get

 

what are the dynamical system which act on invariant manifold?

Hi,

This sequence of commands works perfectly well

     plotsetup(jpeg, plotoutput=SomeJpegFile);
     plot(x, x=0..1);
     plotsetup(default);


Why this one doesn't create the file SomeJpegFile ?

f := proc()
     plotsetup(jpeg, plotoutput=SomeJpegFile);
     plot(x, x=0..1);
     plotsetup(default);
end proc;

f();


Thanks in advance

Is it a complete set ? How to search matrix?

Dear 

Hope everyone is good. I am face to attaine the converges solution of the attached problem. Please have a look and fix my problem. I am waiting your response

diverges.mw

 

-------------------------------------------------- -------------------------------------------------- -------------------------------------------------- ------------------------- >  >  >  >  >  >  >  >  >  (1) >  (2) >    >  >  (3) >  >  # 1 / حساب مصفوفة (A). (طريقة الجمع) >  >  (4) >  (5) >  >  # ------------------------------------------------- -------------------------- # 2 / حساب مصفوفة (ب) من قبل أدومين بوليس لمصطلح غير الخطية. >  (6) >  (7) >  #Find أدومين بولي: >  (8) >  >  #Find a ماتريسز b ^ (k) و C ^ (k): = A ^ (- 1) * b ^ (k)، ثم ايجاد حل تقريبي Y [k]: = سوم (C ^ (k) [i ] * L [i]، i = 1 .. n ): >  # 1) البحث ب (0) >  >  (9) >  (10) >  # 2) البحث عن ج (0) >  (11) >  (12) >  # 3) البحث عن y (0) >  (13) >  # ------------------------- >  #Find b (1) >  >  >  >  >  (14) >  (15) >  >  # 2) البحث ج (1) >  (16) >

 

تحميل jam.mw

Hi everybody,

I want to solve numerically an ode and I get this error (undocumented on the maplesoft web site https://www.maplesoft.com/support/help/errors/....)

Error, (in sol) maximum number of event iterations reached (100) at t=2.6610663

I understand where this error can come from but the help pages don't say anything to fix this.
There is some stuff about round-off that could help but I don't understand how to use it.

I would be grateful if you provide me some help.
Thanks in advance


Download ErrorWithDsolve.mw

 

 

Dear 

Hope everyone is fine. In attached file I solved system of equations. But the solution like this 

Sol[1]:={{...},{...}}

But I want the solution like

Sol[1]:={...}

Please see the attachment and fix my problem

Problem.mw

Dear

I am facing to eliminate diff(p(x, y), y, x) from Eq1 and Eq2. My procedure is given below:

Eq1 := 2*rho[nf]*a^2*x*(diff(f(eta), eta, eta))*(diff(f(eta), eta))/h+rho[nf]*sqrt(nu[f])*(diff(f(eta), eta))*a*x*(diff(f(eta), eta, eta))/h^2+rho[nf]*sqrt(nu[f])*f(eta)*a*x*(diff(f(eta), eta, eta, eta))/h^2+2*rho[nf]*omega[0]*a*x*(diff(g(eta), eta))/h = -(diff(p(x, y), y, x))+mu[nf]*a*x*(diff(f(eta), eta, eta, eta, eta))/h^3-sigma[nf]*B[0]^2*a*x*(diff(f(eta), eta, eta))/h;

Eq2 := 0 = -(diff(p(x, y), y, x));

eliminate({Eq1, Eq2}, diff(p(x, y), y, x));

Dear 

I want to graw following points (u[i,j], i=0..M,j=0..N) obtained in Sol[i] in 3D where i takes along x-axes, j y-axis and u along z axes. I also want the style of point plot as surface. Same do for v and w. I am waiting your response, Thanks

3D_plots.mw

Dear

I want to draw the graphs of the attached system of PDEs for different values of M in 3D please fix my problem. I am waiting your positive response.

graphs_for_pde.mw