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Finding solutions to the Picard boundary value problem via homotopy method. (English) Zbl 1199.65246
Summary: This paper deals with the problem of finding solutions to the Picard boundary problem. In our approach, by means of the homotopy method, the equation considered is linked to a simpler equation by introducing a parameter. We first find the solutions of the simpler equation, and give a priori estimates of the equation we considered, and then the solutions of Picard boundary problem can be obtained by following the path of solutions of the Cauchy problem.
MSC:
65L10 Numerical solution of boundary value problems involving ordinary differential equations
65H20 Global methods, including homotopy approaches to the numerical solution of nonlinear equations
34B15 Nonlinear boundary value problems for ordinary differential equations
65L70 Error bounds for numerical methods for ordinary differential equations
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