Approximate Analytical Methods in Double Parametric Form Of Fuzzy Numbers for Solving Fuzzy Partial Differential Equations (S/O 14188)
The fuzzy partial differential equations (FPDEs) have practical importance in mathematical modelling involving uncertainty. However, in numerous cases, it is challenging to find their exact solutions. Similar challenge experienced in partial differential equations has brought about the emergence of...
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| Main Authors: | , |
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| Format: | Monograph |
| Language: | English |
| Published: |
UUM
2021
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| Subjects: | |
| Online Access: | https://repo.uum.edu.my/id/eprint/31561/1/14188.pdf https://repo.uum.edu.my/id/eprint/31561/ |
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| Summary: | The fuzzy partial differential equations (FPDEs) have practical importance in mathematical modelling involving uncertainty. However, in numerous cases, it is challenging to find their exact solutions. Similar challenge experienced in partial differential equations has brought about the emergence of approximate analytical methods for solving them. These methods are also known to have fast convergence rate. Approximate analytical method can even handle problems which may not have exact solutions. Difficult problems can be solved without the need to compare with the exact solution to determine the accuracy of the obtained approximate solution. In solving FPDEs, it is common to employ the single parametric form of fuzzy numbers. However, double parametric form is more general and straightforward with lower complexity. Therefore, this study has developed new approximate analytical methods in double parametric form of fuzzy numbers based on the original crisp Homotopy Perturbation Method, Variational Iteration Method, Homotopy Analysis Method and Optimal Homotopy Asymptotic Method to solve FPDEs involving fuzzy heat equation, fuzzy reaction-diffusion equation and fuzzy wave equation. In constructing the new methods, the original methods in single parametric form have been studied in their crisp cases, followed by their development in double parametric form of fuzzy numbers for FPDEs. Validation of the convergence of the solution of the constructed methods have been done either through comparison with exact solution or through residual error. The developed methods can be used to solve real problems that can be modelled by FPDEs such as in the area of meteorology and electromagnetic field |
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