A novel numerical scheme for reproducing kernel space of 2D fractional diffusion equations

Siyu Tian; Boyu Liu; Wenyan Wang; Siyu Tian; Boyu Liu; Wenyan Wang

doi:10.3934/math.20231488

AIMS Mathematics

2023, Volume 8, Issue 12: 29058-29072. doi: 10.3934/math.20231488

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Research article

A novel numerical scheme for reproducing kernel space of 2D fractional diffusion equations

Department of Mathematics, Northeast Forestry University, Harbin 150040, China

Received: 18 June 2023 Revised: 19 October 2023 Accepted: 19 October 2023 Published: 26 October 2023
MSC : 35A40, 65N35, 65R20

A novel method is presented for reproducing kernel of a 2D fractional diffusion equation. The exact solution is expressed as a series, which is then truncated to get an approximate solution. In addition, some techniques to improve existing methods are also proposed. The proposed approach is easy to implement. It is proved that both the approximate solution and its partial derivatives converge to their exact solutions. Numerical results demonstrate that the proposed approach is effective and can provide a high precision global approximate solution.
- exact solution,
- numerical method,
- 2D fractional diffusion equations,
- reproducing kernel
Citation: Siyu Tian, Boyu Liu, Wenyan Wang. A novel numerical scheme for reproducing kernel space of 2D fractional diffusion equations[J]. AIMS Mathematics, 2023, 8(12): 29058-29072. doi: 10.3934/math.20231488

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Abstract

A novel method is presented for reproducing kernel of a 2D fractional diffusion equation. The exact solution is expressed as a series, which is then truncated to get an approximate solution. In addition, some techniques to improve existing methods are also proposed. The proposed approach is easy to implement. It is proved that both the approximate solution and its partial derivatives converge to their exact solutions. Numerical results demonstrate that the proposed approach is effective and can provide a high precision global approximate solution.

References

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