Abstract
In this article, boundary value problems of second order linear ordinary differen- tial equations are solved directly using hybrid block one-step method. Power series of order six is adopted as basis function to derive this method through collocation and interpolation approach. Shooting method is employed to transform boundary value problem into initial value problem. Then hybrid block one step is used to approximate the solution. The perfor- mance of the new method is shown by solving some boundary value problems examined by previous methods.
Highlights
Mathematical models are expressed by boundary value problem (BVPs) and initial value problem (IVPs) of ordinary differential equations in order to help
Several numerical methods have been derived to approximate the solutions for BVPs
It worth to highlight that, one step hybrid block method combines the advantages of block and hybrid methods( see [2], [5]) which overcomes the zero stability barrier in linear multistep method [3]
Summary
Mathematical models are expressed by boundary value problem (BVPs) and initial value problem (IVPs) of ordinary differential equations in order to help. Several numerical methods have been derived to approximate the solutions for BVPs. According to [7], the using of spline methods for solving BVPs was initially investigated by Bickley in 1968. In 2002, [8] proposed different finite numerical method for solving two-point BVPs. Recently, [10] presented three-points block one-step method for solving second order linear Dirichlet and Neumann BVPs directly. [10] presented three-points block one-step method for solving second order linear Dirichlet and Neumann BVPs directly These methods have dealt with some difficulties for solving BVPs which leads to inefficiently in term of error. It worth to highlight that, one step hybrid block method combines the advantages of block and hybrid methods( see [2], [5]) which overcomes the zero stability barrier in linear multistep method [3]
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