Solving Fractional Generalized Fisher–Kolmogorov–Petrovsky–Piskunov’s Equation Using Compact-Finite Different Methods Together with Spectral Collocation Algorithms
The main target of this work is presenting two efficient accurate algorithms for solving numerically one of the most important models in physics and engineering mathematics, Fisher–Kolmogorov–Petrovsky–Piskunov’s equation (Fisher-KPP) with fractional order, where the derivative operator is defined a...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/1901131 |
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| author | Maged Z. Youssef M. M. Khader Ibrahim Al-Dayel W. E. Ahmed |
| author_facet | Maged Z. Youssef M. M. Khader Ibrahim Al-Dayel W. E. Ahmed |
| author_sort | Maged Z. Youssef |
| collection | DOAJ |
| description | The main target of this work is presenting two efficient accurate algorithms for solving numerically one of the most important models in physics and engineering mathematics, Fisher–Kolmogorov–Petrovsky–Piskunov’s equation (Fisher-KPP) with fractional order, where the derivative operator is defined and studied by the fractional derivative in the sense of Liouville–Caputo (LC). There are two main processes; in the first one, we use the compact finite difference technique (CFDT) to discretize the derivative operator and generate a semidiscrete time derivative and then implement the Vieta–Lucas spectral collocation method (VLSCM) to discretize the spatial fractional derivative. The presented approach helps us to transform the studied problem into a simple system of algebraic equations that can be easily resolved. Some theoretical studies are provided with their evidence to analyze the convergence and stability analysis of the presented algorithm. To test the accuracy and applicability of our presented algorithm a numerical simulation is given. |
| format | Article |
| id | doaj-art-df3689c1256d4bae9ebee663633cbd95 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-df3689c1256d4bae9ebee663633cbd952025-02-03T06:10:54ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/1901131Solving Fractional Generalized Fisher–Kolmogorov–Petrovsky–Piskunov’s Equation Using Compact-Finite Different Methods Together with Spectral Collocation AlgorithmsMaged Z. Youssef0M. M. Khader1Ibrahim Al-Dayel2W. E. Ahmed3Department of Mathematics and StatisticsDepartment of Mathematics and StatisticsDepartment of Mathematics and StatisticsDepartment of Mathematics and StatisticsThe main target of this work is presenting two efficient accurate algorithms for solving numerically one of the most important models in physics and engineering mathematics, Fisher–Kolmogorov–Petrovsky–Piskunov’s equation (Fisher-KPP) with fractional order, where the derivative operator is defined and studied by the fractional derivative in the sense of Liouville–Caputo (LC). There are two main processes; in the first one, we use the compact finite difference technique (CFDT) to discretize the derivative operator and generate a semidiscrete time derivative and then implement the Vieta–Lucas spectral collocation method (VLSCM) to discretize the spatial fractional derivative. The presented approach helps us to transform the studied problem into a simple system of algebraic equations that can be easily resolved. Some theoretical studies are provided with their evidence to analyze the convergence and stability analysis of the presented algorithm. To test the accuracy and applicability of our presented algorithm a numerical simulation is given.http://dx.doi.org/10.1155/2022/1901131 |
| spellingShingle | Maged Z. Youssef M. M. Khader Ibrahim Al-Dayel W. E. Ahmed Solving Fractional Generalized Fisher–Kolmogorov–Petrovsky–Piskunov’s Equation Using Compact-Finite Different Methods Together with Spectral Collocation Algorithms Journal of Mathematics |
| title | Solving Fractional Generalized Fisher–Kolmogorov–Petrovsky–Piskunov’s Equation Using Compact-Finite Different Methods Together with Spectral Collocation Algorithms |
| title_full | Solving Fractional Generalized Fisher–Kolmogorov–Petrovsky–Piskunov’s Equation Using Compact-Finite Different Methods Together with Spectral Collocation Algorithms |
| title_fullStr | Solving Fractional Generalized Fisher–Kolmogorov–Petrovsky–Piskunov’s Equation Using Compact-Finite Different Methods Together with Spectral Collocation Algorithms |
| title_full_unstemmed | Solving Fractional Generalized Fisher–Kolmogorov–Petrovsky–Piskunov’s Equation Using Compact-Finite Different Methods Together with Spectral Collocation Algorithms |
| title_short | Solving Fractional Generalized Fisher–Kolmogorov–Petrovsky–Piskunov’s Equation Using Compact-Finite Different Methods Together with Spectral Collocation Algorithms |
| title_sort | solving fractional generalized fisher kolmogorov petrovsky piskunov s equation using compact finite different methods together with spectral collocation algorithms |
| url | http://dx.doi.org/10.1155/2022/1901131 |
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