A0 -STABLE RATIONAL INTEGRATOR FOR THE SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS
Abstract
This research work is concerned with the determination of solution to different classes of problems in Ordinary Differential Equations (ODEs). We derived an ???????? - Stable rational integrators for the solution of ordinary differential equations. We establish the convergence, consistency and the stability of our scheme in the interpolants of order m = 3, through the rational integrator. The stability analysis of
the method was carried with the use of MAPLE-18 and MATLAB softwares. We compared our new and solve real-life problems which ascertain the convergence and consistency of scheme. Our result shows that our integrator is stable analytically and computationally.
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References
Abhulimen, C. E. (2009): An exponential fitting predictor- corrector formula for stiff systems of Ordinary Differential Equations. International Journal of Computational and Applied Mathematics, vol.4, No 2, 115 – 126.
Ebhohimen F. and Anetor O. (2017);The Stability of the Rational Interpolation Method in Ordinary Differential Equations at k = 6.Transactions of the Nigerian Association of Mathematical physics Volume 5, (September and November, (2017);pp 33-38.
Elakhe O. A. and Aashikpelokhai, U.S.U. (2011): On A Singulo Oscillatory-Stiff Rational Integrator. International Journal of Natural and Applied Science, Vol. 8, pp1703-1715.
Elakhe O. A. and Aashikpelokhai, U.S.U. (2013): A High Accuracy Order Three and Four Numerical Integrator for initial value problems, International Journal of Numerical Mathematics,, Vol. 6, pp57 – 71.
Elakhe O. A. (2011):Singulo-Oscillatory Stiff Rational Integrator.Ph.D Thesis, Ambrose Alli University, Ekpoma. 173pp.
Aashikpelokhai, U.S.U (2010): A general [L, M] One-step integrator for Initial Value Problems. International Journal of Computer Mathematics, vol. 1 – 12.
Fatunla, S.O. (1978); “An implicit Two-part numerical integration Formula for linear and non-linear stiff system of ODE”, Mathematics of Computation 32,1-11.
Lambert J.D. (1995): Numerical Methods for Ordinary Differential Systems. John Wiley and Sons Limited, England, 293 pages.
Esekhaigbe, C. A. (2017): On the component analysis and transformation of an explicit fourth-stage fourth-order Runge-Kutta methods.Ph.D Thesis, Ambrose Alli University, Ekpoma. 85pp.
Elakhe O. A ,Ehika, E and Ehika S. (2020): A quartic based denominator of order six rational integrator. J, Physical & Applied Sciences, Vol.2, No 1, Ambrose Alli University, Ekpoma.
Aashikpelokhai, U.S.U (2010): A general [L, M] One- step integrator for Initial Value Problems. International Journal of Computer Mathematics, vol. 1 – 12.
Aashikpelokhai, U.S.U (2014): Renaissance of Mathematics in our Time. Pub. FNS AAU Ekpoma
Ebhohimen F. and Anetor O. (2017);The Stability of the Rational Interpolation Method in Ordinary Differential Equations at k = 6.Transactions of the Nigerian Association of Mathematical physics Volume 5, (September and November, (2017);pp 33-38.
Elakhe, Isere and Ebhohimen Trans. Of NAMP Elakhe O. A ,Ehika, E and Ehika S. (2020): A quartic based denominator of order six rational integrator. J, Physical & Applied Sciences, Vol.2, No 1, Ambrose Alli University, Ekpoma.
Elakhe O.A. and Aashikpelokhai, U.S.U. (2010): On ASingulo-Stiff Rational Integrator. International Journal of Natural and Applied Science, Vol. 2, pp43-53.
Elakhe O. A. (2011):Singulo-Oscillatory Stiff Rational Integrator.Ph.D Thesis, Ambrose Alli University, Ekpoma. 173pp.
Elakhe O. A. and Aashikpelokhai, U.S.U. (2013): On A Singulo Oscillatory-Stiff Rational Integrator. International Journal of Natural and Applied Science, Vol. 8, pp1703-1715.
Esekhaigbe, C. A. (2017): Transformation and Implementation of a Highly Efficient Fully Implicit Forth-Order Runge-Kutta Method. International Journal of Innovative Research, vol 5(1), 171 – 183.
Fatunla, S.O. (1978); “An implicit Two-part numerical integration Formula for linear and non-linear stiff system of ODE”, Mathematics of Computation 32,1-11.
Lambert J.D and Shaw B. (1965): “On the Numerical Solution of y' = f(x,y) by a class of formulae based on Rational Approximation”. Mathematics of Computation19:456- 462.
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