A Robust Diagonally Implicit Block Method for Solving First Order Stiff IVP of ODEs

Abstract

In this work, a block of diagonally implicit backward differentiation method with two off-step points for solving first order stiff initial value problem of ordinary differential equation was derived. In the proposed block method two approximate solution values of yn+1 and yn+2 with two off-step points yn+ 1/2 and yn+3/2  are computed concurrently for each iteration. The properties of the newly proposed method were found to be an A-stable, Zero stable and capable for solving first order Stiff IVPs. To validate the performance of the proposed method, some first order stiff IVPs are solved and the result obtained was compared with other existing numerical schemes. From the tabulated results and the graphs plotted, the proposed method has shown advantages of accuracy in the scale error over the three methods and an advantage of executional time over two of the existing methods considered.