Abstract: This paper focuses on a new extension approach for the construction of Exponential General Linear Methods. These methods are related to Butcher, Calvo and Palencia and Osisiogu and Bazuaye Methods, but, in contrast to the later, we make use of higher terms of the exponential and related matrix functions within the numerical solution and not in the internal stage order extension as done by Osisiogu and Bazuaye. This feature enables us to derive the order conditions which in turn aided in the construction of family of methods of higher order. The stability behavior is consistent with the existing methods but with the advantage of having less computational effort. Numerical experiments indicate that Extended Exponential General Linear Methods constructed via this approach compete favourably with the existing Methods.
Key words: Exponential methods,General Linear Methods, Order Conditions, Stability.
How to cite this article:
Bazuaye F.E and Osisiogu A.U, A New Approach to Constructing Extended Exponential General Linear Methods for Initial Value Problems in Ordinary Differential Equations, International Journal of Advances in Mathematics, Volume 2017, Number 5, Pages 44-54, 2017.