Numerical Technique of Solving Boundary Delay Differential Equations

Abstract

The two-points direct multistep block approach order four is used to approximate the solutions for second order delay differential equations of the constant type with boundary conditions. Direct integration is suggested since reducing the second order equations to first-order equations will require longer computational time. The two-points approximate solutions for each iteration are calculated simultaneously in the block method can minimize computational time. In contrast to the one-step approach, the multistep method frequently proves to be efficient in decreasing the frequency of function calls. Since the concerns involved boundary values, the shooting method is used to determine the guessing of the initial value. The representation of the stability regions is used to analyze the method’s stability. The method’s reliability is observed through four numerical problems.