An efficient method for solving two-point boundary value problems with extremely high accuracy

Abstract

A novel numerical method for solving two-point boundary value problems is presented. This method utilizes a recasting technique for transformation of fundamental differential equations into S-system (synergistic and saturable system) canonical form that consists of a set of simultaneous first-order differential equations, an efficient computational algorithm that was proposed to numerically solve the S-system differential equations, and the shooting method. A two-point boundary value problem associated with an immobilized enzyme reaction was investigated as a model system, and it was found that the accuracy of numerical solutions obtained by the proposed method was almost the same as the accuracy of the computer. Another advantage of the proposed method is that it enables one to write a generalized computer program for two-point boundary value problems. With such a program, the user can solve different types of two-point boundary value problems by just imputing S-system parameters that are obtained by recasting their fundamental differential equations.