Explicit Numerical Methods with Enhanced Stability ‎Properties for First-Order Autonomous Initial-Value ‎Problems

Dr Sameer A Matar's picture
Journal Title, Volume, Page: 
International Journal of Engineering Science Volume 30, Issue 3, Pages 379–392
Year of Publication: 
1992
Authors: 
S.A. Matar
Department of Mathematics, Faculty of Science, An-Najah National University, Nablus, Palestine
Current Affiliation: 
Department of Mathematics, Faculty of Science, An-Najah National University, Nablus, Palestine
E.H. Twizell
Department of Mathematics and Statistics, Brunel University, Uxbridge, Middlesex UB8 3PH, U.K
D.A. Voss
Department of Mathematics, Western Illinois University, Macomb, IL 61455, U.S.A
A.Q.M. Khaliq
Department of Mathematics, Western Illinois University, Macomb, IL 61455, U.S.A
Preferred Abstract (Original): 

First-order numerical methods are developed for the numerical solution of systems of autonomous, first-order, initial-value problems. The approach followed yields a formulation which is implicit but which, it is seen, can be implemented explicitly. Numerical results are obtained for three problems from the scientific literature, including the Lorenz equations and initial-value problems ansing in the thermal decomposition of ozone and double-diffusive convection. The implicit derivation of the methods allows a larger time-step to be used in computing the solutions, than that used by the Euler method which, for some problems, is known to induce contrived chaos in the numerical solution. The use of a larger time-step, without inducing contrived chaos, makes the proposed method more economical than the Euler method which is also first-order.