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Zbl 1032.65084
Khuri, S.A.
A new approach to Bratu's problem. (English)
[J] Appl. Math. Comput. 147, No.1, 131-136 (2004). ISSN 0096-3003

Summary: A Laplace transform decomposition numerical algorithm is introduced for solving Bratu's problem. The numerical scheme is based on the application of the Laplace transform integral operator to the differential equation. The nonlinear term is then decomposed and an iterative algorithm is constructed for the determination of the infinite series solution. The technique is illustrated with two numerical examples and the results show that the method converges rapidly and approximates the exact solution very accurately using only few iterates of the recursive scheme.

MSC 2000:: *65L10 Boundary value problems for ODE (numerical methods)
34B15 Nonlinear boundary value problems of ODE
65L20 Stability of numerical methods for ODE

Keywords: convergence; Laplace transform decomposition numerical algorithm; Bratu's problem; iterative algorithm; infinite series solution; numerical examples

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Zentralblatt MATH Berlin [Germany]