Two-Step Implicit Higher Order Numerical Integrator for Stiff Systems of Initial -Boundary Value Problems of Ordinary Differential Equations

In this paper, a Two-step Implicit Higher order Numerical Integrator was developed for the numerical solution of Stiff Systems of initial-boundary value problems of Ordinary Differential Equations. The exponentially fitted numerical method was derived using collocation approach and the trapezoidal basis as interpolant for the numerical integration for stiff system. The resulting discrete method preserves the A-stability property of numerical scheme and is also L-stable. The local truncation error of the method is estimated from the continuous form of the method derived and presented. The analysis and numerical experiments show clearly that the method compete favourably with known methods when applied to stiff system of initial-boundary value problems of ordinary differential equations. The method is of at least order four (Oh4) in accuracy.