Numerical Treatment of General Third Order Ordinary Differential Equations Using Taylor Series as Predictor
B. G. Ogunware *
Department of Mathematical Sciences, Federal University of Technology Akure, Nigeria.
D. O. Awoyemi
Department of Physical Sciences, Landmark University, Omu-Aran, Kwara State, Nigeria.
L. O. Adoghe
Department of Mathematics, Ambrose Alli University, Ekpoma, Delta State, Nigeria.
O. O. Olanegan
Department of Physical Sciences, Landmark University, Omu-Aran, Kwara State, Nigeria.
E. O. Omole
Department of Mathematical Sciences, Federal University of Technology Akure, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This work considers the direct solution of general third order ordinary differential equation. The method is derived by collocating and interpolating the approximate solution in power series. A single hybrid three-step method is developed. Taylor series is used to generate the independent solution at selected grid and off grid points. The order, zero stability and convergence of the method were established. The developed method is then applied to solve some initial value problems of third order ODEs. The numerical results of the method confirm the superiority of the new method over the existing method.
Keywords: Collocation, interpolation, hybrid, error constant, zero stability, linear multistep method