A New L-Stable Third Derivative Hybrid Method for Solving First Order Ordinary Differential Equations
Lawrence Osa Adoghe *
Department of Mathematics, Ambrose Alli University, Ekpoma, Edo state, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In this paper, an L-stable third derivative multistep method has been proposed for the solution of stiff systems of ordinary differential equations. The continuous hybrid method is derived using interpolation and collocation techniques of power series as the basis function for the approximate solution. The method consists of the main method and an additional method which are combined to form a block matrix and implemented simultaneously. The stability and convergence properties of the block were investigated and discussed. Numerical examples to show the efficiency and accuracy of the new method were presented.
Keywords: Third derivative, L-stable, continuous hybrid methods, block matrix, stiff system