Items tagged with integral-equation

I can't get Simpson's Rule to work properly in Maple for f(x)=cos(e^-x)

According to Wolfram Alpha, I should be getting something like -0.5. Clearly that's not what I'm getting. Please help?

> f := proc (x) options operator, arrow; cos(6*exp(-x)) end proc;
x -> cos(6 exp(-x))

S := evalf(int(f(x), x = 0 .. 1));
                         -0.4411788573
S1 := evalf((1/6)*(1+0)*(f(0)+4*f(1)+f(2)));
                         -0.1215440391
S2 := evalf((1/12)*(1+0)*(f(0)+4*f(1)+2*f(2)+4*f(3)+f(4)));
                          0.3979663797
S-S1;
                         -0.3196348182
100*(S-S1)/S;
                          72.45016685
S-S2;
                         -0.8391452370
100*(S-S2)/S;
                          190.2052247

 

hi,

how we can use maple to find solution of singuler integral equation by using product nystrom method or toeplitz method in maple?

I have the following integral equation to solve numerically:

 

v(x,t)=1 - h*\int_0^t JacobiTheta0(1/2x , \pi i s) v^4(1,t-s)ds

where h is a numerical parameter, and v(1,t) = 1-h*\int_0^t \theta_3(r)v^4(1,t-r)dr (theta3 is Jacobi theta3 function).

 

So I want to use an iteration method that will converge numerically to the solution, where v(1,0)=1.

How to use maple for this?

I want also to find the rate of convergence to the numerical solution.

 edit: I should note that v(x,0)=1, even though it's implied from v(x,t) above.

 

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