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References (18)
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Solving Frontier Problems of Physics: The Decomposition Method -
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Numerical study of fisher's equation by Adomian's methodMathematical and Computer Modelling, 19
- Publisher
- Emerald Publishing
- Copyright
- Copyright © 2000 MCB UP Ltd. All rights reserved.
- ISSN
- 0368-492X
- DOI
- 10.1108/03684920010322244
- Publisher site
- See Article on Publisher Site
Abstract
In some papers G. Adomian has presented a decomposition technique in order to solve different non‐linear equations. The solution is found as an infinite series quickly converging to accurate solutions. The method is well‐suited for physical problems and it avoids linearization, perturbation and other restrictions, methods and assumptions which may change the problem being solved – sometimes seriously – unnecessarily. Proofs of convergence are given by Cherruault and co‐authors. Many numerical studies for physical phenomena, such as Fisher’s equation, Lorentz’s equation and Edem’s equation are given and solved. In this work, the general equation given by ∂ p \ o v e r ∂ t = (∇ ⋅(q(x)⋅ ∇p)) + f(x, t) is solved by using decomposition methods, and is compared to other techniques. This equation can be used to describe the motion of a fluid flow in the so‐called reservoir region, where p(x, t) represents the pressure distribution, f(x, t) describes the withdrawal or injection of the fluid, and q(x) is the transmissibility in the reservoir region.
Journal
Kybernetes – Emerald Publishing
Published: Jun 1, 2000
Keywords: Cybernetics; Decomposition method