How can I solve raychaudhuri equations numerically using GRtensor?

g := (-12*y^2+1)/(4*y^2+1)^3 * ln(abs(-1+2^(1-x-I*y)));

Compute Int(g, [x=1/2 .. infinity, y=0 .. infinity]).

PS: this stems from How to calculate hard integral?, 
but it is not related to the RH.

Hi. I want to generate a Julia set, and teh first instruction in the demo, applications fractal is

GenerateComplex(a,b,c,d,e)

I have Maple13 and I can not find such instruction. Could you tell me where can I get it, or how to define it?

Thanks

Help Please! :)
As it is seen in the picture, I can not integrate the power series. In contrast, the differentiation works!
what is wrong?

 support type error when plot, and moreover how to animate this plot

restart;
with(ExcelTools):
with(ListTools):
with(DynamicSystems):
filename := "0257.HK";
open3 := Import(cat(cat("C://Temp//HK//Bank//",filename),".xls"), filename, "B2:B100");
high3 := Import(cat(cat("C://Temp//HK//Bank//",filename),".xls"), filename, "C2:C100");
low3 := Import(cat(cat("C://Temp//HK//Bank//",filename),".xls"), filename, "D2:D100");
close3 := Import(cat(cat("C://Temp//HK//Bank//",filename),".xls"), filename, "E2:E100");
with(CurveFitting):
n := 31;
f := Vector(n);
f2 := Vector(n);
open2 := Vector(n);high2 := Vector(n);gain2 := Vector(n);algebra2 := Vector(n);creative2 := Vector(n);creative3 := Vector(n);
upper2 := Vector(n);lower2 := Vector(n);upperloweratio := Vector(n);
deltaopen2 := Vector(n); deltahigh2 := Vector(n); deltalow2 := Vector(n); deltaclose2 := Vector(n);
logn := Vector(n);
for i from 0 to n-4 do
open2[i+1] := PolynomialInterpolation([[0,open3[n-i][1]],[1,open3[n-(i+1)][1]],[2,open3[n-(i+2)][1]],[4,open3[n-(i+3)][1]]],t):
high2[i+1] := PolynomialInterpolation([[0,high3[n-i][1]],[1,high3[n-(i+1)][1]],[2,high3[n-(i+2)][1]],[4,high3[n-(i+3)][1]]],t):
low2[i+1] := PolynomialInterpolation([[0,low3[n-i][1]],[1,low3[n-(i+1)][1]],[2,low3[n-(i+2)][1]],[4,low3[n-(i+3)][1]]],t):
if (close3[i+1][1]/close3[i+2][1]-1) < 0 then
gain2[i+1] := -1*round(100*abs(close3[i+1][1]/close3[i+2][1]-1)):
else
gain2[i+1] := round(abs(100*(close3[i+1][1]/close3[i+2][1]-1))):
end if;
od;
n := 31;
newclose := Vector(n);
for j from 0 to n-4 do
for i from 0 to n-4 do
x1 := close3[i+1];
y1 := close3[i+1];
newclose[i+1] := subs(y=y1, subs(x=x1, (1/2)*(-y+sqrt(-3*y^2-4*y*x))/y))
od;
close3 := newclose;
plot(close3(x), x=1..31);
od;

Hi, I have a bivariate generating function that looks like this

where x is enumerating by binary strings by length and k is counting a number patterns in the string. I would like to convert the series into partial fractions. Convert[parfrac] only seems to work when k is given a value, which I did for several small small choices, from which I guessed the general partial fraction decomposition. Would someone have an idea on how to extract the partial fractions directly in terms of x and k?

Thanks,

best, Luke

Hello all!

I have to solve 1D Heat equation with Neumann B.C. using implicit scheme.

I have: 

I have my code in Maple for the solution of this problem using explicit sceme for Neumann B.C.. And I also have the solution of the problem using implicit scheme(but for Dirichle B.C.).

implicit_method_Dirichle_B.C..mws
explicit_method_Neumann_B.C..mws

I know that my Neumann B.C. for implicit scheme will be written like this.
I determined the ghost points and then got the final view of the B.Cs.:

But I can not imagine how I should put my Neumann  B.C. for implicit scheme in the code. 

Please, help me! I will be very grateful!

Hi,

Can anyone help me to solve this system of equations in Maple?

solve({
(-(1*Rfd*(1-(Ladssec/Lfd)+((((1.007033 +1*(Laqssec+Ll))*Ladssec)/(((Ra+0.04527646)^2+(1.007033 +1*(Ladssec+Ll))*(1.007033 +1*(Laqssec+Ll)))*Lfd)) *Ladssec)))/(Lfd))=-0.0069
,(-(1*Rfd*(-(Ladssec/Lfd)+((((1.007033 +1*(Laqssec+Ll))*Ladssec)/(((Ra+0.04527646)^2+(1.007033 +1*(Ladssec+Ll))*(1.007033 +1*(Laqssec+Ll)))*L1d)) *Ladssec)))/(Lfd))=0.002689
,(-(1*Rfd*(-((Ra+0.04527646)/((Ra+0.04527646)^2+(1.007033 +1*(Ladssec+Ll))*(1.007033 +1*(Laqssec+Ll))))*(Laqssec/L1q))*Ladssec)/(Lfd))=0.00002647
,(-(1*Rfd*(-((Ra+0.04527646)/((Ra+0.04527646)^2+(1.007033 +1*(Ladssec+Ll))*(1.007033 +1*(Laqssec+Ll))))*(Laqssec/L2q)) *Ladssec)/(Lfd))=-0.00001362

,(-(1*R1d*(-(Ladssec/Lfd)+((((1.007033 +1*(Laqssec+Ll))*Ladssec)/(((Ra+0.04527646)^2+(1.007033 +1*(Ladssec+Ll))*(1.007033 +1*(Laqssec+Ll)))*Lfd))*Ladssec)))/(L1d))=0.1052
,(-(1*R1d*(1-(Ladssec/Lfd)+((((1.007033 +1*(Laqssec+Ll))*Ladssec)/(((Ra+0.04527646)^2+(1.007033 +1*(Ladssec+Ll))*(1.007033 +1*(Laqssec+Ll)))*L1d)) *Ladssec)))/(L1d))=-0.2585
,(-(1*R1d*(-((Ra+0.04527646)/((Ra+0.04527646)^2+(1.007033 +1*(Ladssec+Ll))*(1.007033 +1*(Laqssec+Ll))))*(Laqssec/L1q))*Ladssec)/(L1d))=0.0009122
,(-(1*R1d*(-((Ra+0.04527646)/((Ra+0.04527646)^2+(1.007033 +1*(Ladssec+Ll))*(1.007033 +1*(Laqssec+Ll))))*(Laqssec/L2q)) *Ladssec)/(L1d))=-0.0005093

,(-(1*R1q*(((Ra+0.04527646)/((Ra+0.04527646)^2+(1.007033 +1*(Ladssec+Ll))*(1.007033 +1*(Laqssec+Ll))))*(Ladssec/Lfd))*Laqssec)/(L1q))=-0.000292
,(-(1*R1q*(-((Ra+0.04527646)/((Ra+0.04527646)^2+(1.007033 +1*(Ladssec+Ll))*(1.007033 +1*(Laqssec+Ll))))*(Ladssec/L1d))*Laqssec)/(L1q))=0.0008507
,(-(1*R1q*(1-(Laqssec/L1q)+((((1.007033 +1*(Ladssec+Ll))*Laqssec)/(((Ra+0.04527646)^2+(1.007033 +1*(Ladssec+Ll))*(1.007033 +1*(Laqssec+Ll)))*L1q))*Laqssec)))/(L1q))=-0.04423
,(-(1*R1q*(-(Laqssec/L2q)+((((1.007033 +1*(Ladssec+Ll))*Laqssec)/(((Ra+0.04527646)^2+(1.007033 +1*(Ladssec+Ll))*(1.007033 +1*(Laqssec+Ll)))*L2q))*Laqssec)))/(L1q))=0.0003831

,(-(1*R2q*(((Ra+0.04527646)/((Ra+0.04527646)^2+(1.007033 +1*(Ladssec+Ll))*(1.007033 +1*(Laqssec+Ll))))*(Ladssec/Lfd))*Laqssec)/(L2q))=-0.001785
,(-(1*R2q*(-((Ra+0.04527646)/((Ra+0.04527646)^2+(1.007033 +1*(Ladssec+Ll))*(1.007033 +1*(Laqssec+Ll))))*(Ladssec/L1d))*Laqssec)/(L2q))=-0.03134
,(-(1*R2q*(-(Laqssec/L1q)+((((1.007033 +1*(Ladssec+Ll))*Laqssec)/(((Ra+0.04527646)^2+(1.007033 +1*(Ladssec+Ll))*(1.007033 +1*(Laqssec+Ll)))*L1q))*Laqssec)))/(L2q))=4.239
,(-(1*R2q*(1-(Laqssec/L2q)+((((1.007033 +1*(Ladssec+Ll))*Laqssec)/(((Ra+0.04527646)^2+(1.007033 +1*(Ladssec+Ll))*(1.007033 +1*(Laqssec+Ll)))*L2q))*Laqssec)))/(L2q))=-4.868

}, {L1d, L1q, Ladssec, Laqssec, Lfd, R1d, R1q, Rfd, Ra, Ll},useassumptions)

assuming Lfd ~= 0.1632, R1d~=0.0269, L1d~=0.0750, L1q~=-0.1350, Ladssec~=0.0500, Laqssec~= -0.1500, Rfd~=0.0016, R1q~= 0.0215, Ra~=0.005, Ll~=0.15

which theory can explain the interaction of composition of group for combination of composition of group

if succeed to search a list of groups, what is the next step research them?

Hi,

I have a linear system to solve.

mm:=proc(a,x,h,i)
local A,Z1,Z2,Z,F,result;  # to declare the local variable
A:=array(1..2,1..2,[[1,1],[a,a+h]]);
Z1:=evalf(int(1/(abs(y-x)+.000000001),y=a..a+h));
Z2:=evalf(int(y/(abs(y-x)+.000000001),y=a..a+h));
Z:=array([Z1,Z2]);
F:=evalm(inverse(A)&*Z);
result:=F[i]
end:

My questions: 

1) My exact Z1 is Z1:=evalf(int(1/(abs(y-x)),y=a..a+h)); but I ask if can I put

Z1:=evalf(int(1/(abs(y-x)+.000000001),y=a..a+h));

the same for Z2.

2) Can I writte in a simple form the vector Z.  Because, later, il have a second system contains Z1,Z2, Z3, Z4,Z5.  The difference between Z1 and Z2 is the variable "y" added in the integral of Z2.

Many thinks.

I wish to  plot 2D animate for the soltion of this equation here is the code

restart;
with(PDEtools):
with(ArrayTools):
with(plots):

f:=u->sech(u):
g:=v->sech(v):
h:=1/10:
N:=20:
M:=20:
V:=x->x^2:
psi:=Array(0..N/h+1,0..M/h+1):
for i from 0 to N/h do
psi[i,0]:=evalf(f(i*h)):
od:
for j from 0 to M/h do
psi[0,j]:=evalf(g(j*h)):
od:
for i from 1 to N/h do
for j from 1 to M/h do
psi[i,j]:=-psi[i-1, j-1]+(1-(1/8)*h^2*V((1/2)*h*(j-i-1)))*psi[i, j-1]+(1-(1/8)*h^2*V((1/2)*h*(j- i+1)))*psi[i-1,j]:
od:
od:
ls:=[seq([seq([i*h,j*h,psi[i,j]],i=0..N/h)],j=0..M/h)]:

surfdata((ls),axes=boxed,labels=[`u`,`v`,`psi(u,v)`],shading=zhue,style=patchcontour);

Hey, 

I am trying to write a single procedure to find the root of any function using the Newton-Raphson method, given the initial approximation and the tolerance. If this fails to converge, the program must then use the Bisection method to find the root. Need some help please. The current procedure i have done is only coming out with the first Iteration 

Thanks for the help!

how to singularize existing function?

any group theory can describe the singularity function?

Good day, please how can one solve these BVPs using FINITE DIFFERENCE METHOD in maple. Here is the problem FDM.mw

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