Generalized enright-type symmetric methods for the solution of boundary value problems

Abstract

This study details the modification and generalization of the conventional Enright method to achieve highly stable symmetric boundary value methods (BVMs) with improved order ($k+3$) and accuracy for the numerical solution of boundary value problems (BVPs). BVMs are natural candidate for the solution of BVPs when constructed well. The class of methods developed herein is of the family of second derivative linear multistep formulas (LMF). Most LMF available for the numerical solution of BVPs are either of first derivative or specialized higher derivative. However, such schemes give little or no room for modifications to improve order, stability and accuracy, hence, the literature available for numerical solutions of BVPs is not nearly plentiful compared with the vast literature for initial value problems (IVPs). The new class of methods poses to be very promising as it possesses the potential of being more accurate for the same order than the usual prominent symmetric BVMs found in the literature. The numerical experimentations of the new scheme on standard BVPs emphasized their usefulness.