Numerical Solution of Stiff and Oscillatory Differential Equations Using a Block Integrator
J. Sunday *
Department of Mathematical Sciences, Adamawa State University, Mubi, Nigeria.
M. R. Odekunle
Department of Mathematics, Modibbo Adama University of Technology, Yola, Nigeria.
A. A. James
Department of Mathematics, American University of Nigeria, Yola, Nigeria.
A. O. Adesanya
Department of Mathematics, Modibbo Adama University of Technology, Yola, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This paper presents the derivation and implementation of a block integrator for the solution of stiff and oscillatory first-order initial value problems of Ordinary Differential Equations (ODEs). The integrator was derived by collocation and interpolation of the combination of power series and exponential function to generate a continuous implicit Linear Multistep Method (LMM). The basic properties of the derived integrator were investigated and the integrator was implemented on some sampled stiff and oscillatory problems. From the results obtained, it is obvious that the block integrator gives better approximation than some existing ones.
Keywords: Block Integrator, Exponential Function, Oscillatory, Power Series, Stiff.