New Generalized Jacobi Galerkin Operational Matrices of Derivatives: An Algorithm for Solving Multi-Term Variable-Order Time-Fractional Diffusion-Wave Equations
The current study discusses a novel approach for numerically solving MTVO-TFDWEs under various conditions, such as IBCs and DBCs. It uses a class of GSJPs that satisfy the given conditions (IBCs or DBCs). One of the important parts of our method is establishing OMs for Ods and VOFDs of GSJPs. The se...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-01-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/8/1/68 |
| _version_ | 1797343955199721472 |
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| author | Hany Mostafa Ahmed |
| author_facet | Hany Mostafa Ahmed |
| author_sort | Hany Mostafa Ahmed |
| collection | DOAJ |
| description | The current study discusses a novel approach for numerically solving MTVO-TFDWEs under various conditions, such as IBCs and DBCs. It uses a class of GSJPs that satisfy the given conditions (IBCs or DBCs). One of the important parts of our method is establishing OMs for Ods and VOFDs of GSJPs. The second part is using the SCM by utilizing these OMs. This algorithm enables the extraction of precision and efficacy in numerical solutions. We provide theoretical assurances of the treatment’s efficacy by validating its convergent and error investigations. Four examples are offered to clarify the approach’s practicability and precision; in each one, the IBCs and DBCs are considered. The findings are compared to those of preceding studies, verifying that our treatment is more effective and precise than that of its competitors. |
| first_indexed | 2024-03-08T10:55:18Z |
| format | Article |
| id | doaj.art-6c86e61413db406fb2fcf9a12f096936 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-08T10:55:18Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-6c86e61413db406fb2fcf9a12f0969362024-01-26T16:36:40ZengMDPI AGFractal and Fractional2504-31102024-01-01816810.3390/fractalfract8010068New Generalized Jacobi Galerkin Operational Matrices of Derivatives: An Algorithm for Solving Multi-Term Variable-Order Time-Fractional Diffusion-Wave EquationsHany Mostafa Ahmed0Department of Mathematics, Faculty of Technology and Education, Helwan University, Cairo 11281, EgyptThe current study discusses a novel approach for numerically solving MTVO-TFDWEs under various conditions, such as IBCs and DBCs. It uses a class of GSJPs that satisfy the given conditions (IBCs or DBCs). One of the important parts of our method is establishing OMs for Ods and VOFDs of GSJPs. The second part is using the SCM by utilizing these OMs. This algorithm enables the extraction of precision and efficacy in numerical solutions. We provide theoretical assurances of the treatment’s efficacy by validating its convergent and error investigations. Four examples are offered to clarify the approach’s practicability and precision; in each one, the IBCs and DBCs are considered. The findings are compared to those of preceding studies, verifying that our treatment is more effective and precise than that of its competitors.https://www.mdpi.com/2504-3110/8/1/68Jacobi polynomialsfractional differential equations with variable ordercollocation methodinitial boundary conditionsDirichlet boundary conditions |
| spellingShingle | Hany Mostafa Ahmed New Generalized Jacobi Galerkin Operational Matrices of Derivatives: An Algorithm for Solving Multi-Term Variable-Order Time-Fractional Diffusion-Wave Equations Fractal and Fractional Jacobi polynomials fractional differential equations with variable order collocation method initial boundary conditions Dirichlet boundary conditions |
| title | New Generalized Jacobi Galerkin Operational Matrices of Derivatives: An Algorithm for Solving Multi-Term Variable-Order Time-Fractional Diffusion-Wave Equations |
| title_full | New Generalized Jacobi Galerkin Operational Matrices of Derivatives: An Algorithm for Solving Multi-Term Variable-Order Time-Fractional Diffusion-Wave Equations |
| title_fullStr | New Generalized Jacobi Galerkin Operational Matrices of Derivatives: An Algorithm for Solving Multi-Term Variable-Order Time-Fractional Diffusion-Wave Equations |
| title_full_unstemmed | New Generalized Jacobi Galerkin Operational Matrices of Derivatives: An Algorithm for Solving Multi-Term Variable-Order Time-Fractional Diffusion-Wave Equations |
| title_short | New Generalized Jacobi Galerkin Operational Matrices of Derivatives: An Algorithm for Solving Multi-Term Variable-Order Time-Fractional Diffusion-Wave Equations |
| title_sort | new generalized jacobi galerkin operational matrices of derivatives an algorithm for solving multi term variable order time fractional diffusion wave equations |
| topic | Jacobi polynomials fractional differential equations with variable order collocation method initial boundary conditions Dirichlet boundary conditions |
| url | https://www.mdpi.com/2504-3110/8/1/68 |
| work_keys_str_mv | AT hanymostafaahmed newgeneralizedjacobigalerkinoperationalmatricesofderivativesanalgorithmforsolvingmultitermvariableordertimefractionaldiffusionwaveequations |