A Modified Block Adam Moulton (MOBAM) Method for the Solution of Stiff Initial Value Problems of Ordinary Differential Equations

Abstract

Stiff ordinary differential equations pose computational difficulties as they present severe step size restrictions on the numerical methods to be used. Construction of numerical methods that possess suitable stability properties for the solution of such systems has been the target of many researchers. Development of methods suitable for these systems of equations has been either through the use of derivative of the solution or by introducing off-step points, additional stages or super future points. These processes have been exploited in Runge-Kutta methods or linear multistep methods. In this study, an improved class of linear multistep block method has been constructed based on Adams Moulton block methods. The improved methods are shown to be A-stable, a property desirable to handle stiff ODEs. Methods of uniform orders 10 and 11 have been constructed. The efficiency of the new methods tested on stiff systems of ODEs and the results reveal that the MOBAM methods compare favourably with results obtained using the state of the art Matlab Ode23 solver.