Proper Generalized Decomposition Method for Solving Fisher-Type Equation and Heat Equation
- Autores: Isaac C.1
-
Afiliações:
- Dept. of Mechanical Engineering
- Edição: Volume 10, Nº 1 (2018)
- Páginas: 120-133
- Seção: Article
- URL: https://journals.rcsi.science/2070-0482/article/view/202139
- DOI: https://doi.org/10.1134/S2070048218010039
- ID: 202139
Citar
Resumo
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.
Sobre autores
Chukwuemeke Isaac
Dept. of Mechanical Engineering
Autor responsável pela correspondência
Email: cw.isaac@ui.edu.ng
Nígeria, Ibadan