An Application of Second Derivative Backward Differentiation Formula Hybrid Block Method on Stiff Ordinary Differential Equations

Abstract

In this paper, we developed a continuous scheme of four and five step with one off-grid point at collocation which provides the approximate solution of both linear and nonlinear stiff ordinary differential equations with constant step size. The continuous scheme is evaluated at both interpolation and collocation where necessary to give continuous hybrid block scheme and high order of accuracy with low error constants. Numerical results of the schemes are presented to compare with exact solutions and the results have shown that the (SDHBBDF) performed favorably when compare with existing methods.

Keywords: Collocation and interpolation, Hybrid block methods, Second Derivative and Stiff systems