الملخص الإنجليزي
Abstract
Practical mathematical problems are usually nonlinear in nature and it is well known that solutions to many nonlinear ordinary differential equations would require some sort of numerical treatment. The standard approach is to use single or multistep methods with or without predictor-corrector mode. In recent years, the idea of using block methods to numerically solve nonlinear differential equations has been receiving a lot of attention. Many variation of block methods with varying orders, both explicit and implicit, have been developed and studied.
In this work, we shall look at some of the block methods in detail including the derivations and order of these methods. The stability and convergence properties
of the methods are included and then illustrate the performance of these block
methods with a traditional multistep method in predictor-corrector mode for some
nonlinear initial value problems.
