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

Özet

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 differentialequations which exhibit a phenomenon which has come to be known as stiffness. In this work, a new four-stepexponentially-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 techniqueof exponential fitting. The constructed method is well-suited for systems with pronounced stiffness. The stabilityproperty of the constructed scheme is also considered. To investigate the accuracy of the constructed method, threestandard numerical examples with pronounced stiffness are considered. A comparison of the results obtained byimplementing the proposed methods on the numerical problems compared with those of existing standard methodshow that the constructed method is efficient and accurate for solving stiff systems of ordinary differential equations.