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Finite difference spectral collocation schemes for the solutions of Bratu's problem
  • Adebayo Adewumi,
  • Adebayo Aderogba
Adebayo Adewumi
Obafemi Awolowo University
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Adebayo Aderogba
Obafemi Awolowo University

Corresponding Author:[email protected]

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Abstract

This paper is concerned with new methods based on standard and nonstandard finite difference schemes for solving one-dimensional Bratu’s problem numeri- cally. Using quasilinearization technique, the original problem is converted into a sequence of linear problems. Chebyshev polynomials are employed to ap- proximate the second order derivative of function, y(x), after which Sumudu transform is applied to obtain a new form of trial function and this is then substituted into a linearized and discretized Bratu’s equation. We discuss the convergence analysis of the methods and also compare the numerical results with those obtained by other existing methods. The results show that the pro- posed methods yield accurate approximations to the exact solution of Bratu’s problem.