Direct Integrator for Fifth order Boundary Value Problems in Ordinary Differential Equations

Mark I.  Modebei; Raphael B.  Adeniyi; Samuel  Jator

Mark I. Modebei Department of Mathematics, University of Ilorin, P.M.B 1515, Ilorin, Nigeria.
Raphael B. Adeniyi Department of Mathematics, University of Ilorin, P.M.B 1515, Ilorin, Nigeria.
Samuel Jator Department of Mathematics and Statistics, Austin Peay State University Clarksville, TN 37044

Keywords: Boundary Value Problems, Block Methods, Convergence, Linear multistep.

Abstract

Fifth-order Boundary Value Problems (BVPs) in Ordinary Differential Equations are solved using Block Unification Methods (BUM). Continuous Linear Multistep Methods (CLMMs) are developed via the collocation and interpolation approach. These methods constitutes the main and additional methods which are unified in block fashion for numerically solving general fifth order linear and nonlinear BVPs in ODEs. The method is analyzed for its order, local trucation error, consistency and its convergence. Sufficient numerical evidences were given to show the effectiveness of the new scheme in terms of accuracy and flexibility. Some numerical examples are used to show the robustness in handling such problems. The method performed favourably well viz-a-viz other existing methods in literature.

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