| Autor: |
Dauda GuliburYAKUBU, Abubakar Muhammad KWAMI, AbdulHamid Muhammad GAZALI, Abdu Ibrahim MAKSHA |
| Jazyk: |
angličtina |
| Rok vydání: |
2012 |
| Předmět: |
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| Zdroj: |
Leonardo Journal of Sciences, Vol 11, Iss 21, Pp 13-32 (2012) |
| ISSN: |
1583-0233 |
| Popis: |
Accurate solutions to initial value systems of ordinary differential equations may be approximated efficiently by Runge-Kutta methods or linear multistep methods. Each of these has limitations of one sort or another. In this paper we consider, as a middle ground, the derivation of continuous general linear methods for solution of stiff systems of initial value problems in ordinary differential equations. These methods are designed to combine the advantages of both Runge-Kutta and linear multistep methods. Particularly, methods possessing the property of A-stability are identified as promising methods within this large class of general linear methods. We show that the continuous general linear methods are self-starting and have more ability to solve the stiff systems of ordinary differential equations, than the discrete ones. The initial value systems of ordinary differential equations are solved, for instance, without looking for any other method to start the integration process. This desirable feature of the proposed approach leads to obtaining very high accuracy of the solution of the given problem. Illustrative examples are given to demonstrate the novelty and reliability of the methods. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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