Multi-derivative hybrid methods for integration of general second order differential equations

Sunday Jacob Kayode; Abejide Kolawole Success

doi:10.26637/MJM0704/0042

Abstract

In this study, new multi-derivative hybrid methods for the integration of general second order initial value problems of ordinary differential equations are considered. Linear multistep formula was used in the development of the methods taking Taylor series as the basis function. The unknown parameters were solved by the systematic reduction of simultaneous nonlinear equations. Due to the lapses in number of equations compared to the number of unknowns, we make $\beta_0=0$ as a free parameter. Analysis of the resulting methods shows that they are zero stable, consistent and convergent. Numerical examples are given to demonstrate and compare the efficiency of the methods for the stepnumbers $k=1$ and $k=2$ respectively. The results shows a better performance on existing methods.

Keywords:

Initial value problems, Ordinary differential equation, Linear Multistep Method, Taylor series.

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

Sunday Jacob Kayode Department of Mathematical Sciences, Federal University of Technology, Akure.
Abejide Kolawole Success Department of Mathematical Sciences, Federal University of Technology, Akure.

Pages: 877-882
Date Published: 01-10-2019
Vol. 7 No. 04 (2019): Malaya Journal of Matematik (MJM)

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