Abstract
In this paper, a well-known computer algebra system (CAS) was considered for the derivation of Numerical method for the solution of initial value problems. This was achieved by the use of maple software. Numerical methods were derived through Lagrange interpolation method. Both the implicit and explicit method was derived with the help of the Computer algebra system. In particular, a review of Maple’s functional role in the derivation of numerical methods was also presented. The main challenge was that the efficient handling and simplifying of very long expressions, which was met by the power of Maple’s build-in functionality. The use of the maple procedure had significantly reduced the errors and hence improved efficiency in derivation of higher order Adams Methods.
Highlights
The most popular multistep formulas in use today are based on numerical integration, by means of suitably chosen polynomial interpolation formulas
Adams methods has been introduced in this paper, we obtained an implicit and explicit Adams Method through the use of symbolic algebra system called Maple
The interesting part of paper is the symbolic construction of Adams Methods which was used to generate a set of all explicit and implicit Linear Multistep Adams methods, otherwise known as predictor and corrector method for approximate solution of initial value problem for ordinary differential equations
Summary
The most popular multistep formulas in use today are based on numerical integration, by means of suitably chosen polynomial interpolation formulas. [1] is a general purpose system, designed to handle a wide variety of problems Maple has known capability amongs are the symbolic computation, polynomial operations, symbolic differentiation, integration and solving algebraic equations, exact solution for ODEs/PDEs. Several researchers have uses Maple code to derived or manipulate some symbolic expression, [2], uses Maple to investigated on how computer algebra system can be employ for research and development study in the biology, [3], uses somes Maple capabilities to derived a kinematic relations for robot. Several researchers were involved in employing the symbolic algebra system, where [5] investigated the symbolic computation for use in stochastic numerics has been developed. All useful Lagrange interpolation formula can be computed without difficulty, in contrast to hand derivatives, which usually end with only few points. The Algorithm in Appendix 1 and 2, sample statements serve to illustrate some of Maple's syntax
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