Development of an Order (k+3) Block-Hybrid Linear Multistep Method for the Direct Solution of General Second Order Initial Value Problems

Authors

  • F Muritala Department of Mathematics, Federal University of Technology Minna, Niger State
  • M.K. Kolawole Department of Mathematical Sciences, Osun State University, Osogbo , Osun State
  • A.A Oyedeji Department of Mathematics, Federal University of Technology Minna, Niger State)
  • J.O. Lawal Department of Mathematics, Federal University of Technology Minna, Niger State
  • A.I. Alaje Department of Mathematical Sciences, Osun State University, Osogbo , Osun State

DOI:

https://doi.org/10.36108/ujees/2202.40.0230

Keywords:

Block-Hybrid, Collocation, LMM,, Power series, Second Order IVPs

Abstract

Block hybrid linear multistep method was proposed to overcome the Dahl Quist order barrier for linear multistep methods. This research aims to answer questions relating to the convergence, accuracy, and effectiveness of the block hybrid method when utilized to obtain the solution of Initial Value Problems (IVPs). In this research, an order (k+3) block hybrid method applicable to obtain the direct solution of IVP’s of ordinary differential equations (ODEs) is presented. Collocation and interpolation of power series at finely selected grid points were used to improve the method's consistency, convergence, accuracy and zero stability. Linear problems were
solved to show the accuracy and efficiency of the proposed method, and the error obtained from the comparison of exact and approximate results shows that the proposed method is effective in solving the class of problem.

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Published

2025-11-21

Issue

Vol. 4 No. 2 (2022): Volume 4, Number 2, 2022

Section

Articles