An Order 2k Hybrid Backward Differentiation Formula for Stiff System of Ordinary Differential Equations Using Legendre Polynomial as Basis Function

Abstract

In this paper, a k-step, (k=2, 3, 4), Block Hybrid Backward Differentiation Formula for the solution of Stiff systems of Ordinary Differential Equation have been formulated through continuous collocation approach. 𝑘 off - grid points were incorporated at interpolation in order to retain the single function evaluation characteristic, which is peculiar to Backward Differentiation Formula. The basic properties of numerical methods were analyzed and the methods were found to be consistent with a uniform order 2𝑘, zero stable and as such, convergent. The region of absolute stability of the methods were analyzed using the general linear method (GLM), and found to be stable over a large region. The methods compute the solution of Stiff systems in a block-by block way by some discrete schemes obtained from the associated continuous scheme which are combined and implemented as a set of block formulae. Numerical experiments were carried out and the results obtained, were compare with the exact or analytical solutions and some methods found in literatures.