Academic Journal
A higher order stable numerical approximation for time‐fractional non‐linear Kuramoto–Sivashinsky equation based on quintic B‐‐spline: A higher order stable numerical approximation for time-fractional non-linear Kuramoto-Sivashinsky equation based on quintic \(\mathfrak{B}\)-spline
| Title: | A higher order stable numerical approximation for time‐fractional non‐linear Kuramoto–Sivashinsky equation based on quintic B‐‐spline: A higher order stable numerical approximation for time-fractional non-linear Kuramoto-Sivashinsky equation based on quintic \(\mathfrak{B}\)-spline |
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| Authors: | Renu Choudhary, Satpal Singh, Pratibhamoy Das, Devendra Kumar |
| Source: | Mathematical Methods in the Applied Sciences. 47:11953-11975 |
| Publisher Information: | Wiley, 2024. |
| Publication Year: | 2024 |
| Subject Terms: | convergence, L1-2 scheme, Nonlinear higher-order PDEs, stability analysis, Fractional partial differential equations, 01 natural sciences, Caputo derivative, time varying layer, L1 scheme, Burgers' equation, Initial-boundary value problems for second-order parabolic equations, 0101 mathematics, computational cost, higher order splines, time-fractional Kuramoto-Sivashinsky equation |
| Description: | This article deals with designing and analyzing a higher order stable numerical analysis for the time‐fractional Kuramoto–Sivashinsky (K‐S) equation, which is a fourth‐order non‐linear equation. The fractional derivative of order present in the considered problem is taken into Caputo sense and approximated using the scheme. In space direction, the discretization process uses quintic ‐spline functions to approximate the derivatives and the solution of the problem. The present approach is unconditionally stable and is convergent with rate of accuracy , where and denote the space and time step sizes, respectively. We have also noted that the linearized version of the K‐S equation leads the rate of accuracy to . The present approach is also highly effective for the time‐fractional Burgers' equation. We have shown that the present approach provides better accuracy than the scheme with the same computational cost for several linear/non‐linear problems, with classical as well as fractional time derivatives. |
| Document Type: | Article |
| File Description: | application/xml |
| Language: | English |
| ISSN: | 1099-1476 0170-4214 |
| DOI: | 10.1002/mma.9778 |
| Rights: | Wiley Online Library User Agreement |
| Accession Number: | edsair.doi.dedup.....54542b9f70a7d90bcd4eafc0ce21e11a |
| Database: | OpenAIRE |
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