A Reduced-Order Extrapolation Spectral-Finite Difference Scheme Based on the POD Method for 2D Second-Order Hyperbolic Equations. Issue 5 (3rd September 2017)

• Record Type: Journal Article
• Authors: Luo, Zhendong; Jin, Shiju
• Is Part Of: Mathematical modelling and analysis. Volume 22:Issue 5(2017)
• Page Start: 569
• Page End: 586
• Publication Date: 2017-09-03
• Subjects: reduced-order extrapolation spectral-finite difference scheme -- proper orthogonal decomposition -- second-order hyperbolic equations -- classical spectral-finite difference method -- error estimates; 65N12 -- 65M15 -- 65N30; Mathematical models -- Periodicals; Mathematical models -- Study and teaching -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis -- Problems, exercises, etc -- Periodicals; Mathematical analysis; Mathematical models; Mathematical models -- Study and teaching; Periodicals; Problems and exercises; 511.805
• DOI: 10.3846/13926292.2017.1334714
• Languages: English
• ISSNs: 1392-6292

Abstract

Abstract: In this study, a reduced-order extrapolation spectral-finite difference (ROESFD) scheme based on the proper orthogonal decomposition (POD) method is set up for the two-dimensional (2D) second-order hyperbolic equations. First, the classical spectral-finite difference (CSFD) method for the 2D second-order hyperbolic equations and its stability, convergence, and flaw are introduced. Then, a new ROESFD scheme that has very few degrees of freedom but holds sufficiently high accuracy is set up by the POD method and its implementation is offered. Finally, three numerical examples are offered to explain the validity of the theoretical conclusion. This implies that the ROESFD scheme is viable and efficient for searching the numerical solutions of the 2D second-order hyperbolic equations.