Convergence properties of 3-point block Adams method with one off-step point for ODEs

Abstract

Numerous critical and intricate systems from various disciplines of sciences are developed by means of differential equations. Analytical methods are frequently complex or unfeasible to execute for problems due to the difficulty of these systems, therefore, numerical methods are the way out. To integrate differential equations, the most common approaches are single step and multistep techniques. A well-known multistep method Adams formula is one of the appropriate methods for solving non-stiff ordinary differential equation (ODEs). Present research emphases of 3-Point Block Method with one off-step point using Adams Moulton Formula for finding the solution intended for the system of non-stiff first order ODEs. Block method has been derived by considering the Adams Formula. The development of this method will compute the three solution values at xn+1 , x n+2 and x n+3 comprising of one off-step point at x n+2.5 using constant step size. The advantage of adding up one off-step point in the implicit Adams method will lead us towards better accuracy. This paper is shaped up with the derivation of the formula followed by its convergence properties by using MATHEMATICA software. As a result, the method is consistent and zero-stable, which implies convergence.