Fractal-fractional advection–diffusion–reaction equations by Ritz approximation approach
In this work, we propose the Ritz approximation approach with a satisfier function to solve fractalfractional advection–diffusion–reaction equations. The approach reduces fractal-fractional advection–diffusion– reaction equations to a system of algebraic equations; hence, the system can be solved ea...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Degruter
2023
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| Subjects: | |
| Online Access: | http://eprints.uthm.edu.my/8771/1/J15735_0a978ec0c88b43c83dfa97263e880111.pdf http://eprints.uthm.edu.my/8771/ |
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| Summary: | In this work, we propose the Ritz approximation approach with a satisfier function to solve fractalfractional advection–diffusion–reaction equations. The approach reduces fractal-fractional advection–diffusion– reaction equations to a system of algebraic equations; hence, the system can be solved easily to obtain the numerical solution for fractal-fractional advection–diffusion–reaction equations. With only a few terms of two variables-shifted
Legendre polynomials, this method is capable of providing
high-accuracy solution for fractal-fractional advection–diffusion–reaction equations. Numerical examples show that this
approach is comparable with the existing numerical method.
The proposed approach can reduce the number of terms of
polynomials needed for numerical simulation to obtain the
solution for fractal-fractional advection–diffusion–reaction
equations. |
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