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A numerical algorithm for solving Troesch’s problem. (English) Zbl 1022.65084
Summary: A numerical method based on Laplace transform and a modified decomposition technique is introduced for the approximate solution of B. A. Troesch’s problem [J. Comput. Phys. 21, 279-290 (1976; Zbl 0334.65063)]. The underlying idea of the scheme is to assume an infinite series solution and operate with Laplace transform integral operator to both sides of the differential equation. The nonlinear term is then decomposed, and an iterative algorithm is constructed for the determination of the terms of the infinite series solution. Two special cases of the problem are illustrated and the results show that the method is very accurate and converges rapidly.
MSC:
65L10Boundary value problems for ODE (numerical methods)
34B15Nonlinear boundary value problems for ODE
65L20Stability and convergence of numerical methods for ODE