A Reduced-Dimension Extrapolating Method of Finite Element Solution Coefficient Vectors for Fractional Tricomi-Type Equation-Reference-Cited by-同舟云学术

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

Published:2023-11-20 Issue:22 Volume:11 Page:4699
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Li Yuejie¹²,Luo Zhendong²³^ORCID

Affiliation:

1. Department of Mathematics and Computer Engineering, Ordos Institute of Technology, Ordos 017000, China

2. School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China

3. School of Digitalized Intelligence Engineering, Hunan Sany Polytechnic College, Changsha 410129, China

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.

Funder

Ordos Science and Technology Plan Project

Inner Mongolia Natural Science Foundation

National Natural Science Foundation of China

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/22/4699/pdf

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