ABSTRACT
DERIVATION AND IMPLEMENTATION OF A-STABLE DIAGONALLY IMPLICIT HYBRID BLOCK METHOD FOR THE NUMERICAL INTEGRATION OF STIFF ORDINARY DIFFERENTIAL EQUATIONS
Journal: Matrix Science Mathematic (MSMK)
Author: Alhassan B., Musa H., Yusuf H., Adamu A., Bello A., Hamisu A
This is an open access article distributed under the Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
DOI: 10.26480/msmk.02.2024.59.68
A new 2-point hybrid block method for the numerical solution of first-order stiff systems of ordinary differential equations in initial value problems with optimal stability property is presented. The necessary and sufficient conditions for the convergence of the proposed implicit block numerical scheme for solving stiff ODEs are established. The stability and convergence analysis of the method show that it is consistent, zero-stable, and convergent. The absolute stability region of the method is plotted, indicating that the method is A-stable. The method is implemented in Microsoft Dev C++ environment using the C programming language and Newton’s iteration, and some selected first-order stiff initial value problems are solved. The numerical results obtained for the proposed method are compared with the existing fifth order fully implicit 2-point block backward differentiation formula and 2-point block backward differentiation formula with two off-step points methods. The comparison reveals that the new method outperforms both methods in terms of accuracy but are competing in terms of computation time as we reduce the step size. It is evident that the method converges faster.