Academic Journal
A fast H3N3‐2σ$_\sigma$‐based compact ADI difference method for time fractional wave equations: A fast H3N3-2\(_\sigma\)-based compact ADI difference method for time fractional wave equations
| Title: | A fast H3N3‐2σ$_\sigma$‐based compact ADI difference method for time fractional wave equations: A fast H3N3-2\(_\sigma\)-based compact ADI difference method for time fractional wave equations |
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| Authors: | Ruilian Du |
| Source: | ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik. 104 |
| Publisher Information: | Wiley, 2024. |
| Publication Year: | 2024 |
| Subject Terms: | Finite difference methods for boundary value problems involving PDEs, Error bounds for initial value and initial-boundary value problems involving PDEs, alternating direction implicit (ADI) schemes, Fractional derivatives and integrals, Numerical interpolation, Smoothness and regularity of solutions to PDEs, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Fractional partial differential equations |
| Description: | In the present paper, we derive a fast H3N3‐2‐based compact alternating direction implicit (ADI) scheme for the time fractional wave equation in two‐dimensional spatial domains. The time fractional derivative involved in the equation is discretized by the H3N3‐2 formula combined with sum‐of‐exponential technique. The former was first proposed by Du et al., while the latter has become a widely used technique to reduce the computational cost in the processing of convolution integrals. The spatial discretization adopts the standard compact ADI method, which can ensure that the space can reach the fourth‐order accuracy without increasing the amount of computation. The numerical stability and convergence of the difference scheme are analyzed rigorously. As an auxiliary illustration, a numerical example is given to verify the validity of the theoretical findings. |
| Document Type: | Article |
| File Description: | application/xml |
| Language: | English |
| ISSN: | 1521-4001 0044-2267 |
| DOI: | 10.1002/zamm.202400431 |
| Rights: | Wiley Online Library User Agreement |
| Accession Number: | edsair.doi.dedup.....483db2e663fdb447a7ae612f17adb05c |
| Database: | OpenAIRE |
| ISSN: | 15214001 00442267 |
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| DOI: | 10.1002/zamm.202400431 |