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- Title
A Review of the Integral Transforms-Based Decomposition Methods and their Applications in Solving Nonlinear PDEs.
- Authors
Nuruddeen, R. I.; Muhammad, Lawal; Nass, A. M.; Sulaiman, T. A.
- Abstract
The integral transform based decomposition method comprises of coupling a particular integral transform defined in a time domain and the well-known Adomian decomposition method (ADM) established by G. Adomian. Though, integral transforms are as old as at least two hundred years, but of recent, many researchers seem to turn their attention to the development of this an old area in the last two decades, and more especially this current one. However, with the emergence of these newly initiated integral transforms and the decomposition method on the other hand; the decomposition methods based on these integral transforms and the just introduced transforms that are yet to be coupled with the ADM will be reviewed and coupled respectively. Further, the decomposition method obtained in each mixture (i.e. based on each integral transform) will be utilized to treat nonlinear partial differential equations (PDEs), as the methods are firmly believed to need no linearization, no discretization and no perturbation among others in comparison with other methods for solving nonlinear differential equations.
- Subjects
PARTIAL differential equations; INTEGRAL transforms; DECOMPOSITION method
- Publication
Palestine Journal of Mathematics, 2018, Vol 7, Issue 1, p262
- ISSN
2219-5688
- Publication type
Article