An efficient numerical scheme in reproducing kernel space for space fractional partial differential equations

Boyu Liu; Wenyan Wang; Boyu Liu; Wenyan Wang

doi:10.3934/math.20241588

AIMS Mathematics

2024, Volume 9, Issue 11: 33286-33300. doi: 10.3934/math.20241588

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Research article

An efficient numerical scheme in reproducing kernel space for space fractional partial differential equations

Boyu Liu ,
Wenyan Wang ^,

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

Received: 29 September 2024 Revised: 09 November 2024 Accepted: 15 November 2024 Published: 22 November 2024
MSC : 35A40, 65N35, 65R20

A numerical approach is proposed for space fractional partial differential equations by the reproducing kernel approach. Some procedures are presented for improving the existing methods. The presented method is easy to accomplish. Approximate solutions and their partial derivatives are shown to converge to exact solutions, respectively. Experiments show that the presented technique is efficient, and that high-precision global approximate solutions can be obtained.
- space fractional partial differential equation,
- reproducing kernel,
- exact solution,
- numerical approach
Citation: Boyu Liu, Wenyan Wang. An efficient numerical scheme in reproducing kernel space for space fractional partial differential equations[J]. AIMS Mathematics, 2024, 9(11): 33286-33300. doi: 10.3934/math.20241588

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Abstract

A numerical approach is proposed for space fractional partial differential equations by the reproducing kernel approach. Some procedures are presented for improving the existing methods. The presented method is easy to accomplish. Approximate solutions and their partial derivatives are shown to converge to exact solutions, respectively. Experiments show that the presented technique is efficient, and that high-precision global approximate solutions can be obtained.

References

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