An Unchanged Basis Function and Preserving Accuracy Crank–Nicolson Finite Element Reduced-Dimension Method for Symmetric Tempered Fractional Diffusion Equation

Xiaoyong Yang and Zhendong Luo ()
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Xiaoyong Yang: School of Digitalized Intelligence Engineering, Hunan Sany Polytechnic College, Changsha 410129, China
Zhendong Luo: School of Digitalized Intelligence Engineering, Hunan Sany Polytechnic College, Changsha 410129, China

Mathematics, 2022, vol. 10, issue 19, 1-13

Abstract: We herein mainly employ a proper orthogonal decomposition (POD) to study the reduced dimension of unknown solution coefficient vectors in the Crank–Nicolson finite element (FE) (CNFE) method for the symmetric tempered fractional diffusion equation so that we can build the reduced-dimension recursive CNFE (RDRCNFE) method. In this case, the RDRCNFE method keeps the same basic functions and accuracy as the CNFE method. Especially, we adopt the matrix analysis to discuss the stability and convergence of RDRCNFE solutions, resulting in the very laconic theoretical analysis. We also use some numerical simulations to confirm the correctness of theoretical results.

Keywords: proper orthogonal decomposition; symmetric tempered fractional diffusion equation; reduced dimension recursive Crank–Nicolson finite element method; stability and convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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