On A Four-Step Exponentially Fitted Scheme for The Solution of Stiff Dfferential Systems

Abstract

Many problems that are often encountered in fields like engineering, mechanics, electronic, astrophysics, chemistry and control theory, yield initial value problems involving systems of ordinary differential equations which exhibit a phenomenon which has come to be known as stiffness. In this work, a new four-step exponentially-fitted predictor-corrector method involving the second derivative for solving system of stiff differential

equations is constructed using a combination of the extended backward differentiation formula and the technique of exponential fitting. The constructed method is well-suited for systems with pronounced stiffness. The stability property of the constructed scheme is also considered. To investigate the accuracy of the constructed method, three standard numerical examples with pronounced stiffness are considered. A comparison of the results obtained by implementing the proposed methods on the numerical problems compared with those of existing standard method show that the constructed method is efficient and accurate for solving stiff systems of ordinary differential equations.

Keywords

• Exponentially fitted,multi-step,stiff system,stability,predictor-corrector

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