A NEW CLASS OF SECOND DERIVATIVE METHODS FOR NUMERICAL INTEGRATION OF STIFF INITIAL VALUE PROBLEMS

C. E. ABHULIMEN, L. A. UKPEBOR

Abstract


A new class of four-step second derivative exponential fitting method of order six for the numerical integration of stiff initial-value problems in ordinary differential equations was constructed. The implicit method possesses free parameters which allow it to be fitted automatically to exponential functions.
For the purpose of effective implementation of the newly proposed method, we adopted the mechanism which splits the method into predictor- corrector schemes. The analysis of the stability of the new method was discussed and it was found to be A-stable.
Finally, some numerical experiments confirming theoretical expectations were provided.
The numerical results show that the new method competes favourably with the existing methods in literature in terms of efficiency and accuracy.
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References


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C.E. Abhulimen, Exponential Fitting Predictor-Corrector formula for stiff systems of Ordinary Differential Equations, International Journal of Computational and Applied Mathematics 4 (2) 115-126, 2009.

C.E. Abhulimen, Exponentially Fitted Third Derivative Three-step methods for Numerical Integration of Stiff Initial value problems, Applied Mathematics and Computation 243 446-453, 2014.

C.E. Abhulimen , A Fifth Order Exponential Fitting Integrator, International Journal of Advanced Materials Science 6 (2) 99-107, 2015.

C.E. Abhulimen and S.A. Okunuga, Exponentially fitted second derivative multipstep method for stiff initial value problem for ODE's, Journal of Engineering Science and Applications 5 36-49, 2008.


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