A Compact Difference-Galerkin Spectral Method of the Fourth-Order Equation with a Time-Fractional Derivative
In this article, we proposed a compact difference-Galerkin spectral method for the fourth-order equation in multi-dimensional space with the time-fractional derivative order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantic...
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MDPI AG
2025-03-01
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| Online Access: | https://www.mdpi.com/2504-3110/9/3/155 |
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| author | Yujie Wang Shichao Yi |
| author_facet | Yujie Wang Shichao Yi |
| author_sort | Yujie Wang |
| collection | DOAJ |
| description | In this article, we proposed a compact difference-Galerkin spectral method for the fourth-order equation in multi-dimensional space with the time-fractional derivative order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>∈</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula>. The novel compact difference-Galerkin spectral method can effectively address the issue of high-order derivative accuracy and handle complex boundary problems. Simultaneously, the main conclusions of this article, including the stability, convergence, and solvability of the method, are derived. Finally, some computational experiments are illustrated to demonstrate the superiority of the compact difference-Galerkin spectral method. |
| format | Article |
| id | doaj-art-dcd4beb6c82a4220b69d880f5e0e2dbd |
| institution | DOAJ |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-dcd4beb6c82a4220b69d880f5e0e2dbd2025-08-20T02:42:32ZengMDPI AGFractal and Fractional2504-31102025-03-019315510.3390/fractalfract9030155A Compact Difference-Galerkin Spectral Method of the Fourth-Order Equation with a Time-Fractional DerivativeYujie Wang0Shichao Yi1School of Science, Jiangsu University of Science and Technology, Zhenjiang 212003, ChinaSchool of Science, Jiangsu University of Science and Technology, Zhenjiang 212003, ChinaIn this article, we proposed a compact difference-Galerkin spectral method for the fourth-order equation in multi-dimensional space with the time-fractional derivative order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>∈</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula>. The novel compact difference-Galerkin spectral method can effectively address the issue of high-order derivative accuracy and handle complex boundary problems. Simultaneously, the main conclusions of this article, including the stability, convergence, and solvability of the method, are derived. Finally, some computational experiments are illustrated to demonstrate the superiority of the compact difference-Galerkin spectral method.https://www.mdpi.com/2504-3110/9/3/155Galerkin spectral methodtime-fractional ordervariable coefficient fourth-order equation |
| spellingShingle | Yujie Wang Shichao Yi A Compact Difference-Galerkin Spectral Method of the Fourth-Order Equation with a Time-Fractional Derivative Fractal and Fractional Galerkin spectral method time-fractional order variable coefficient fourth-order equation |
| title | A Compact Difference-Galerkin Spectral Method of the Fourth-Order Equation with a Time-Fractional Derivative |
| title_full | A Compact Difference-Galerkin Spectral Method of the Fourth-Order Equation with a Time-Fractional Derivative |
| title_fullStr | A Compact Difference-Galerkin Spectral Method of the Fourth-Order Equation with a Time-Fractional Derivative |
| title_full_unstemmed | A Compact Difference-Galerkin Spectral Method of the Fourth-Order Equation with a Time-Fractional Derivative |
| title_short | A Compact Difference-Galerkin Spectral Method of the Fourth-Order Equation with a Time-Fractional Derivative |
| title_sort | compact difference galerkin spectral method of the fourth order equation with a time fractional derivative |
| topic | Galerkin spectral method time-fractional order variable coefficient fourth-order equation |
| url | https://www.mdpi.com/2504-3110/9/3/155 |
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