An A- Stable Block Integrator Scheme for the Solution of First Order System of IVP of Ordinary Differential Equations
Muhammad Abdullahi *
Department of Mathematical Sciences, Federal University Dutsinma, Katsina State, Nigeria.
Shamsuddeen Suleiman
Department of Mathematical Sciences, Federal University Dutsinma, Katsina State, Nigeria.
Abdu Masanawa Sagir
Department of Mathematical Sciences, Federal University Dutsinma, Katsina State, Nigeria.
Bashir Sule
Department of Mathematical Sciences, Federal University Dutsinma, Katsina State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In this article, we present an A- stable block integrator scheme for the solution of first order system of IVP of ordinary differential equations. The block scheme at a single integration step produces four approximate solution values of yn+1, yn+2, yn+3 and yn+4 at point xn+1, xn+2, xn+3 and xn+4 respectively. The order and stability property of the scheme are checked, the method is zero stable, A–stable and of order 6. Some test problems are solved with the proposed scheme and the result are compared with some existing method. The proposed method found to have advantages in terms of accuracy, minimum errors and less computational time. Hence, the method is recommended for solving first order system of IVP of ordinary differential equations.
Keywords: Zero stable, A-stable, IVPs, order, ordinary differential equation