A semi-numerical technique for solving the multi-point boundary value problems and engineering applications

Purpose - Multi-point boundary value problems have important. roles in the modelling of various problems in physics and engineering. This paper aims to present the solution of ordinary differential equations with multi-point boundary value conditions by means of a semi-numerical approach which is based on the homotopy analysis method. Design/methodology/approach - The convergence of the obtained solution is expressed and some typical examples are employed to illustrate validity, effectiveness and flexibility of this procedure. This approach, in contrast to perturbation techniques, is valid even for systems without any small/large parameters and therefore it can be applied more widely than perturbation techniques, especially when there do not exist any small/large quantities. Findings - Unlike other analytic techniques, this approach provides a convenient way to adjust and control the convergence of approximation series. Some applications will be briefly introduced. Originality/value - The paper shows how an important boundary value problem is solved with a semi-analytical method.