Wavelet Numerical Solutions for a Class of Elliptic Equations with Homogeneous Boundary Conditions
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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display=&q...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/12/1381 |
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| author | Jinru Wang Wenhui Shi Lin Hu |
| author_facet | Jinru Wang Wenhui Shi Lin Hu |
| author_sort | Jinru Wang |
| collection | DOAJ |
| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></semantics></math></inline-formula> 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. |
| first_indexed | 2024-03-10T10:24:09Z |
| format | Article |
| id | doaj.art-2acf4b5d6fa1469091c1a280c7a7624f |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T10:24:09Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-2acf4b5d6fa1469091c1a280c7a7624f2023-11-22T00:06:53ZengMDPI AGMathematics2227-73902021-06-01912138110.3390/math9121381Wavelet Numerical Solutions for a Class of Elliptic Equations with Homogeneous Boundary ConditionsJinru Wang0Wenhui Shi1Lin Hu2Department of Mathematics, Beijing University of Technology, Beijing 100124, ChinaDepartment of Mathematics, Beijing University of Technology, Beijing 100124, ChinaInstitute of Fundamental and Interdisciplinary Sciences, Beijing Union University, Beijing 100101, ChinaThis 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></semantics></math></inline-formula> 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.https://www.mdpi.com/2227-7390/9/12/1381B-spline waveletselliptic equationhomogeneous boundary conditionnumerical solutionsconvergence |
| spellingShingle | Jinru Wang Wenhui Shi Lin Hu Wavelet Numerical Solutions for a Class of Elliptic Equations with Homogeneous Boundary Conditions Mathematics B-spline wavelets elliptic equation homogeneous boundary condition numerical solutions convergence |
| title | Wavelet Numerical Solutions for a Class of Elliptic Equations with Homogeneous Boundary Conditions |
| title_full | Wavelet Numerical Solutions for a Class of Elliptic Equations with Homogeneous Boundary Conditions |
| title_fullStr | Wavelet Numerical Solutions for a Class of Elliptic Equations with Homogeneous Boundary Conditions |
| title_full_unstemmed | Wavelet Numerical Solutions for a Class of Elliptic Equations with Homogeneous Boundary Conditions |
| title_short | Wavelet Numerical Solutions for a Class of Elliptic Equations with Homogeneous Boundary Conditions |
| title_sort | wavelet numerical solutions for a class of elliptic equations with homogeneous boundary conditions |
| topic | B-spline wavelets elliptic equation homogeneous boundary condition numerical solutions convergence |
| url | https://www.mdpi.com/2227-7390/9/12/1381 |
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