Numerical Simulation for a Multidimensional Fourth-Order Nonlinear Fractional Subdiffusion Model with Time Delay
The purpose of this paper is to develop a numerical scheme for the two-dimensional fourth-order fractional subdiffusion equation with variable coefficients and delay. Using the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><seman...
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MDPI AG
2021-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/23/3050 |
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| author | Sarita Nandal Mahmoud A. Zaky Rob H. De Staelen Ahmed S. Hendy |
| author_facet | Sarita Nandal Mahmoud A. Zaky Rob H. De Staelen Ahmed S. Hendy |
| author_sort | Sarita Nandal |
| collection | DOAJ |
| description | The purpose of this paper is to develop a numerical scheme for the two-dimensional fourth-order fractional subdiffusion equation with variable coefficients and delay. Using the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>L</mi><mn>2</mn></msub><mo>−</mo><msub><mn>1</mn><mi>σ</mi></msub></mrow></semantics></math></inline-formula> approximation of the time Caputo derivative, a finite difference method with second-order accuracy in the temporal direction is achieved. The novelty of this paper is to introduce a numerical scheme for the problem under consideration with variable coefficients, nonlinear source term, and delay time constant. The numerical results show that the global convergence orders for spatial and time dimensions are approximately fourth order in space and second-order in time. |
| first_indexed | 2024-03-10T04:47:59Z |
| format | Article |
| id | doaj.art-04d2700790db47eaa0267099d7d19bb9 |
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| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T04:47:59Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
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| spelling | doaj.art-04d2700790db47eaa0267099d7d19bb92023-11-23T02:45:17ZengMDPI AGMathematics2227-73902021-11-01923305010.3390/math9233050Numerical Simulation for a Multidimensional Fourth-Order Nonlinear Fractional Subdiffusion Model with Time DelaySarita Nandal0Mahmoud A. Zaky1Rob H. De Staelen2Ahmed S. Hendy3Technology Studies Department, Woosong University, Jayang-Dong, Dong-Gu, Daejeon 300-718, KoreaDepartment of Mathematics, Nazarbayev University, Nur-Sultan 010000, KazakhstanBeheer en Algemene Directie, Ghent University Hospital, C. Heymanslaan 10, 9000 Ghent, BelgiumDepartment of Mathematics, Faculty of Science, Benha University, Benha 13511, EgyptThe purpose of this paper is to develop a numerical scheme for the two-dimensional fourth-order fractional subdiffusion equation with variable coefficients and delay. Using the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>L</mi><mn>2</mn></msub><mo>−</mo><msub><mn>1</mn><mi>σ</mi></msub></mrow></semantics></math></inline-formula> approximation of the time Caputo derivative, a finite difference method with second-order accuracy in the temporal direction is achieved. The novelty of this paper is to introduce a numerical scheme for the problem under consideration with variable coefficients, nonlinear source term, and delay time constant. The numerical results show that the global convergence orders for spatial and time dimensions are approximately fourth order in space and second-order in time.https://www.mdpi.com/2227-7390/9/23/3050nonlinear fractional differential equation of fourth-order<i>L</i><sub>2</sub> − 1<i><sub>σ</sub></i> formulatwo-dimensionalvariable coefficientsdelay |
| spellingShingle | Sarita Nandal Mahmoud A. Zaky Rob H. De Staelen Ahmed S. Hendy Numerical Simulation for a Multidimensional Fourth-Order Nonlinear Fractional Subdiffusion Model with Time Delay Mathematics nonlinear fractional differential equation of fourth-order <i>L</i><sub>2</sub> − 1<i><sub>σ</sub></i> formula two-dimensional variable coefficients delay |
| title | Numerical Simulation for a Multidimensional Fourth-Order Nonlinear Fractional Subdiffusion Model with Time Delay |
| title_full | Numerical Simulation for a Multidimensional Fourth-Order Nonlinear Fractional Subdiffusion Model with Time Delay |
| title_fullStr | Numerical Simulation for a Multidimensional Fourth-Order Nonlinear Fractional Subdiffusion Model with Time Delay |
| title_full_unstemmed | Numerical Simulation for a Multidimensional Fourth-Order Nonlinear Fractional Subdiffusion Model with Time Delay |
| title_short | Numerical Simulation for a Multidimensional Fourth-Order Nonlinear Fractional Subdiffusion Model with Time Delay |
| title_sort | numerical simulation for a multidimensional fourth order nonlinear fractional subdiffusion model with time delay |
| topic | nonlinear fractional differential equation of fourth-order <i>L</i><sub>2</sub> − 1<i><sub>σ</sub></i> formula two-dimensional variable coefficients delay |
| url | https://www.mdpi.com/2227-7390/9/23/3050 |
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