[Python] Why is Sinc-Interpolation with Double Exponential Transform not showing exponential...

I’m working on numerically solving the boundary value problem:

u''(x) - u(x) = sin(pi x), for x ∈ [-1,1]
with u(-1) = u(1) = 0


I'm applying Sinc-Interpolation with the Double Exponential (DE) transformation as described in Stenger's method. I construct the second derivative matrix D^(2) in the t-domain, then transform it to the x-domain using:

D_x^(2) = diag(1 / phi'(t_k)^2) * D_t^(2) - diag(phi''(t_k) / phi'(t_k)^3) * D_t^(1)


I solve the linear system:

(D_x^(2) - I) * u = f


after applying Dirichlet boundary conditions at x = ±1. The exact solution is:

u(x) = -sin(pi x) / (pi^2 + 1)


However, even after increasing N to 50 or more, I don’t observe exponential convergence in the max error. The error seems to stagnate.

What could be going wrong? Am I missing something in the transform or derivative matrix? I’d love to hear from anyone who has implemented Sinc collocation with DE successfully.

Thanks in advance!

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