High-order methods for systems of fractional ordinary differential equations and their application to time-fractional diffusion equations
Taking into account the regularity properties of the solutions of fractional differential equations, we develop a numerical method which is able to deal, with the same accuracy, with both smooth and nonsmooth solutions of systems of fractional ordinary differential equations of the Caputo-type. We p...
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| Other Authors: | , , |
| Format: | article |
| Language: | eng |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://hdl.handle.net/1822/66733 |
| Country: | Portugal |
| Oai: | oai:repositorium.sdum.uminho.pt:1822/66733 |
| Summary: | Taking into account the regularity properties of the solutions of fractional differential equations, we develop a numerical method which is able to deal, with the same accuracy, with both smooth and nonsmooth solutions of systems of fractional ordinary differential equations of the Caputo-type. We provide the error analysis of the numerical method and we illustrate its feasibility and accuracy through some numerical examples. Finally, we solve the time-fractional diffusion equation using a combination of the method of lines and the newly developed hybrid method. |
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