Multi-derivative hybrid methods for integration of general second order differential equations
Authors :
Sunday Jacob Kayode 1 * and Abejide Kolawole Success 2
Author Address :
1,2 Department of Mathematical Sciences, Federal University of Technology, Akure.
*Corresponding author.
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.
DOI :
Article Info :
Received : October 01, 2019; Accepted : December 10, 2019.
