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A new approach to Bratu’s problem. (English) Zbl 1032.65084
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:
65L10Boundary value problems for ODE (numerical methods)
34B15Nonlinear boundary value problems for ODE
65L20Stability and convergence of numerical methods for ODE