A reduced order extrapolating technique of solution coefficient vectors to collocation spectral method for telegraph equation

Advances in Difference Equations

article

Wang, Hui¹  He, Qingfang¹  Luo, Zhendong² 

[1] Demonstration Center of Experimental Teaching in Comprehensive Engineering, Beijing Union University;School of Mathematics and Physics, North China Electric Power University

关键词: Reduced order extrapolating technique;    Proper orthogonal decomposition;    Telegraph equation;    Stability and convergence;   

DOI  :  10.1186/s13662-020-2535-0

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this article, we mainly develop a reduced order extrapolating model for the solution coefficient vectors of the classical collocation spectral (CCS) scheme to the two-dimensional (2D) telegraph equation by means of a proper orthogonal decomposition (POD). Therefore, we first present the CCS scheme, offer the existence, stability, and error estimates to the SC solutions, and rewrite the CCS scheme into a matrix-form. We then build a reduced order extrapolating collocation spectral (ROECS) model and analyze the existence and stability as well as errors of the ROECS solutions by some matrix tools. We finally verify the reliability and validity of the ROECS model by means of two sets of numerical simulations for the magnetic field produced by two parallel wires with the same voltage.

【 授权许可】

CC BY