Multidomain Legendre-Galerkin Least-Squares Method for Linear Differential Equations with Variable Coefficients
Year: 2020
Author: Yunqing Huang, Yonghui Qin, Heping Ma, Yanping Chen, Yunqing Huang, Heping Ma
Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 3 : pp. 665–688
Abstract
The multidomain Legendre-Galerkin least-squares method is developed for solving linear differential problems with variable coefficients. By introducing a flux, the original differential equation is rewritten into an equivalent first-order system, and the Legendre Galerkin is applied to the discrete form of the corresponding least squares function. The proposed scheme is based on the Legendre-Galerkin method, and the Legendre/Chebyshev-Gauss-Lobatto collocation method is used to deal with the variable coefficients and the right hand side terms. The coercivity and continuity of the method are proved and the optimal error estimate in $H^1$-norm is obtained. Numerical examples are given to validate the efficiency and spectral accuracy of our scheme. Our scheme is also applied to the numerical solutions of the parabolic problems with discontinuous coefficients and the two-dimensional elliptic problems with piecewise constant coefficients, respectively.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2019-0015
Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 3 : pp. 665–688
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Variable coefficient Legendre Galerkin Legendre/Chebyshev-Gauss-Lobatto least squares.
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