Wavelet Numerical Solutions for a Class of Elliptic Equations with Homogeneous Boundary Conditions

Jinru Wang, Wenhui Shi and Lin Hu
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Jinru Wang: Department of Mathematics, Beijing University of Technology, Beijing 100124, China
Wenhui Shi: Department of Mathematics, Beijing University of Technology, Beijing 100124, China
Lin Hu: Institute of Fundamental and Interdisciplinary Sciences, Beijing Union University, Beijing 100101, China

Mathematics, 2021, vol. 9, issue 12, 1-13

Abstract: This paper focuses on a method to construct wavelet Riesz bases with homogeneous boundary condition and use them to a kind of second-order elliptic equation. First, we construct the splines on the interval [ 0 , 1 ] and consider their approximation properties. Then we define the wavelet bases and illustrate the condition numbers of stiffness matrices are small and bounded. Finally, several numerical examples show that our approach performs efficiently.

Keywords: B-spline wavelets; elliptic equation; homogeneous boundary condition; numerical solutions; convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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