On A Four-Step Exponentially Fitted Scheme for The Solution of Stiff Dfferential Systems
On A Four-Step Exponentially Fitted Scheme for The Solution of Stiff Dfferential Systems
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
___
- Abhulimen C.E., Otunta F.O., A sixth order multiderivative multistep methods for stiff systems of differential equations, International Journal of Numerical Mathematics (IJNM), 2(1)(2006), 248–268.
- Abhulimen C.E., A class of exponentially-fitted third derivative methods for solving stiff differential equations, International Journal of Physical Science, 3(8)(2008), 188–193.
- Abhulimen C.E., Omeike G.E., A sixth-order exponentially fitted scheme for the numerical solution of systems of ordinary differential equations, Journal of Applied Mathematics & Bioinformatics, 1(1)(2011), 175–186.
- Cash J.R., On the integration of stiff systems of O.D.E.s using extended backward differentiation formulae, SIAM J. Numer. Math., 34(1980), 235–246.
- Cash J.R., Second derivative extended backward differentiation formulas for the numerical solution of stiff systems, SIAM J. Numerical Anal., 18(1981), 21–36.
- Cash J.R., On exponentially fitting of composite multiderivative linear methods, SIAM J. Numerical Anal., 18(5)(1981), 808–821.
- Curtiss C.F. and Hirschfelder J.D., Integration of stiff equations, Proc. Nat. Acad. Sci., 38(1952), 235–243.
- Ehigie J.O, Okunuga S.A., Sofoluwe A.B, A class of exponentially fitted second derivative extended backward differentiation formula for
solving stiff problems, Fasciculi Mathematici, 51(2013), 71–84.
- Enright W.H., Pryce J.D., Two Fortran Packages for Assessing IV methods, Technical Report 83(16), Department of Computer Science,
University of Toronto, Canada, 1983.
- Jackson L.W., Kenue S.K., A fourth order exponentially fitted method, SIAM J. Numer. Anal., 11(1974), 965–978.
- Lambert J.D., Computational Methods in Ordinary Differential Equations, John Wiley & Sons, New York, 1973.
- Liniger W.S., Willoughby R.A., Efficient integration methods for stiff system of ODEs, SIAM J. Numerical Anal., 7(1970), 47–65.
- Okunuga S.A., A fourth order composite two-step method for stiff problems, International Journal of Computer Mathematics, 72(1)(1999), 39–47.
- Okunuga S.A., A class of multiderivative composite formula for stiff initial value problems, Advances in Modeling & Analysis, 35(2)(1999), 21–32.