Sinc-collocation method with orthogonalization for singular Poisson-like problems

Yin, Guang Yan

doi:10.1090/S0025-5718-1994-1203738-7

Sinc-collocation method with orthogonalization for singular Poisson-like problems
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Math. Comp. 62 (1994), 21-40 Request permission

Abstract:

This paper uses the Sine-collocation method to solve singular Poisson-like problems (a first- or higher-order partial derivative of the exact solution is unbounded on the boundary). A linear system is obtained which is the same as that obtained by using the Sinc-Galerkin method. With a smart choice of the stepsize and the number of the gridpoints, the orthogonalization technique is successfully applied to solve the linear system obtained, and a numerical approximation is obtained with an exponential accuracy $O(\exp ( - c{N^{\frac {1}{2}}}))$, where N is a truncation parameter and c is a constant independent of N.

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