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An efficient technique to find semi-analytical solutions for higher order multi-point boundary value problems. (English) Zbl 1427.34036

Summary: A new semi-analytical algorithm is presented to solve general multi-point boundary value problems. This method can be applied on \(n\) th order linear, nonlinear, singular and nonsingular multi-point boundary value problems. Mathematical base of the method is presented; convergence of the method is proved. Also, the algorithm is applied to solve multi-point boundary value problems including nonlinear sixth-order, nonlinear singular second-order five-point boundary value problems, and a singularly perturbed boundary value problem. Comparison results show that the new method works more accurate than the other methods.

MSC:

34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations

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