A Reduced-Dimension Extrapolating Method of Finite Element Solution Coefficient Vectors for Fractional Tricomi-Type Equation

Yuejie Li () and Zhendong Luo ()
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Yuejie Li: Department of Mathematics and Computer Engineering, Ordos Institute of Technology, Ordos 017000, China
Zhendong Luo: School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China

Mathematics, 2023, vol. 11, issue 22, 1-13

Abstract: We here employ a proper orthogonal decomposition (POD) to reduce the dimensionality of unknown coefficient vectors of finite element (FE) solutions for the fractional Tricomi-type equation and develop a reduced-dimension extrapolating FE (RDEFE) method for the fractional Tricomi-type equation. For this purpose, we first develop an FE method for the fractional Tricomi-type equation and provide the existence, unconditional stability, and error analysis for the FE solutions. We then develop the RDEFE method for the fractional Tricomi-type equation by means of the POD technique and analyze the existence, unconditional stability, and errors for the RDEFE solutions by using the matrix analysis. Lastly, we provide two numerical examples to verify our theoretical results and to explain the advantages of the RDEFE method.

Keywords: proper orthogonal decomposition; classical finite element method; fractional Tricomi-type equation; reduced-dimension extrapolated finite element method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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