Proper Generalized Decomposition Method for Solving Fisher-Type Equation and Heat Equation
- Authors: Isaac C.W.1
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Affiliations:
- Dept. of Mechanical Engineering
- Issue: Vol 10, No 1 (2018)
- Pages: 120-133
- Section: Article
- URL: https://journals.rcsi.science/2070-0482/article/view/202139
- DOI: https://doi.org/10.1134/S2070048218010039
- ID: 202139
Cite item
Abstract
A model reduction technique—the Proper Generalized Decomposition (PGD) for solving time dependent and multidimensional parameters is reviewed and applied to both the Fisher-type equations and the heat equation. Space-time discretization and separated representation technique for obtaining fast convergence computation while maintaining real time is detailed. Three situations of the Fisher-type equation are solved by the PGD and the results show a perfect agreement with the exact solutions. The source term of the heat equation is given a Huxley source and the thermal diffusivity is taken to be linearly dependent of the spatial parameter. The results show how the Fisher-type equation finds application to the heat equation and that the PGD method allows a perfect representation of the temperature distribution defined in a 5-D tensorial product space and time.
About the authors
Chukwuemeke William Isaac
Dept. of Mechanical Engineering
Author for correspondence.
Email: cw.isaac@ui.edu.ng
Nigeria, Ibadan