An Order (K+5) Block Hybrid Backward Differentiation Formula for Solution of Fourth Order Ordinary Differential Equations

Abstract

This paper covers the derivation and implementation of the 4-step linear Multistep method of Block Hybrid Backward Differentiation Formula (BHBDF) for solving fourth-order initial value problems in ordinary differential equations. In the derivation of the proposed numerical method, the utilization of collocation and interpolation points was adopted with Legendre polynomials serving as the fundamental basis function. The 4-step BHBDF developed to solve fourth-order IVPs has a higher order of accuracy (p=9). Furthermore, the proposed numerical block methods are employed directly to solve fourth-order ODEs. In comparison to some existing methods examined in the prior studies, the proposed method has a robust implementation strategy and demonstrate a higher level of accuracy.