Abstract
This paper studied an enhanced 3-point fully implicit super class of block backward differentiation formula for solving stiff initial value problems developed by Abdullahi & Musa and go further to established the necessary and sufficient conditions for the convergence of the method. The method is zero stable, A-stable and it is of order 5. The method is found to be suitable for solving first order stiff initial value problems
Highlights
In science, engineering and social science most of the real life problems are converted into models
A Linear Multi-Step Method is said to be consistent if its order p is greater than or equal to one
All the necessary and sufficient conditions for the convergence of a linear Multistep Method has been tested in this paper on the developed method, Enhanced 3-Point fully implicit block backward differentiation formula and the method satisfied the conditions
Summary
In science, engineering and social science most of the real life problems are converted into models Such models brought stiff ordinary differential equations. Block backward differentiation formula is one of the reliable block numerical methods for obtaining solutions of stiff initial value problems. Discovered block numerical solution of differential equation, Brugano (1998) with solving differential problem by multistep method, Chu and Hamilton (1987) with parallel solution of ODE’s by multistep method, Dalquish (1974). Developed 2 and 3 point implicit methods for solving stiff initial value problem, both methods are zero and A-stable can handle stiff problem with appreciated results. (3) is called Enhanced 3-Point fully implicit super class of block backward differentiation formula for solving first initial value problems. Detailed of derivation and stability analysis of the method can found in (Abdullahi& Musa 2021)
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