On The Error Analysis of The New Formulation of One Step Method Into Linear Multi Step Method For The Solution of Ordinary Differential Equations

Abstract-This paper presents error analysis of the new formulation of one step method into linear multistep method for the solution of ordinary differential equations. Error analysis in one step method is considerably more difficult than linear multistep method due to the loss of linearity in the method especially for Runge Kutta Method that makes no mention of the function which defines the differential equation makes it impossible to define the order of the method independently of the differential equation. The new formulation of one step method into linear multistep method helps us in overcoming the shortcoming of the method. The error constant zero stability consistency and convergence of one step method were determined through a similar process like linear multistep methods.