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Sinc-Galerkin method for numerical solution of the Bratu’s problems. (English) Zbl 1259.65126
Summary: A study of the performance of the Galerkin method using sinc basis functions for solving Bratu’s problem is presented. An error analysis of the presented method is given. The method is applied to two test examples. By considering the maximum, absolute errors in the solutions at the sinc grid points are tabulated in tables for different choices of step size. We conclude that the sinc-Galerkin method converges to the exact solution rapidly, with order $O\left(exp\left(-c\sqrt{n}\right)\right)$ accuracy, where $c$ is independent of $n$.
##### MSC:
 65L15 Eigenvalue problems for ODE (numerical methods) 34L30 Nonlinear ordinary differential operators 34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds for OD operators 65L60 Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE