A New Class of Third Derivative Fourth-Step Exponential Fitting Numerical Integrator for Stiff Differential Equations

  • C. E. Abhulimen Department of Mathematics, Ambrose Alli University, Ekpoma, Edo State , Nigeria.
  • L. A. Ukpebor Department of Mathematics, Ambrose Alli University, Ekpoma, Edo State , Nigeria.
Keywords: Third derivative four-step, exponentially fitted, A-stable and stiff differential equations.

Abstract

In this paper, we construct a new class of four-step third derivative exponential fitting integrator of order six for the numerical integration of stiff initial-value problems of the type: y<sup>Phys.Rev. ime = f(x,y), \:\: y(x<sub>0</sub></sup> ) = y<sub>0</sub>. The implicit method has free parameters which allow it to be fitted automatically to exponential functions. For the purpose of effective implementation of the new proposed method, we adopted the techniques of splitting the method into predictor and corrector schemes. The numerical analysis of the stability of the new method was discussed; the results show that the new method is A-stable. Finally, numerical examples are presented, to show the efficiency and accuracy of the new method

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Published
2018-09-11
How to Cite
Abhulimen, C. E., & Ukpebor, L. A. (2018). A New Class of Third Derivative Fourth-Step Exponential Fitting Numerical Integrator for Stiff Differential Equations. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 2018, 382 - 391. Retrieved from http://ijmso.unilag.edu.ng/article/view/55
Section
Articles