Solving general fourth order ODEs directly using four point block method

Abstract

A four point block method based on Adams type formulae is proposed for solving general fourth order ordinary differential equations (ODEs) directly. This four point block method will be implemented in predictor corrector mode and the corrector will be iterated to convergent. The numerical solution will be computed at four equally steps simultaneously. Most of the existence researches involving higher order ODEs will reduced the problem to a system of first order ODEs and this approach is obviously will enlarge the systems of first order equations. However, the direct method in this research will solved the fourth order ODEs directly without reducing it to first order equations. Lagrange interpolation polynomial was applied in the derivation of the proposed method. The method was implemented using variable step size in order to determine the approximated solutions. Numerical results shown that the four point block method were superior compared to the existing method. It is clearly proved that the four point block is able to produce acceptable results for solving fourth order ODEs.