A new numerical method for solving two-dimensional variable-order anomalous sub-diffusion equation
The novelty and innovativeness of this paper are the combination of reproducing kernel theory and spline, this leads to a new simple but effective numerical method for solving variable-order anomalous sub-diffusion equation successfully. This combination overcomes the weaknesses of piecewis...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
VINCA Institute of Nuclear Sciences
2016-01-01
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| Series: | Thermal Science |
| Subjects: | |
| Online Access: | http://www.doiserbia.nb.rs/img/doi/0354-9836/2016/0354-983616701J .pdf |
| Summary: | The novelty and innovativeness of this paper are the combination of
reproducing kernel theory and spline, this leads to a new simple but
effective numerical method for solving variable-order anomalous sub-diffusion
equation successfully. This combination overcomes the weaknesses of piecewise
polynomials that can not be used to solve differential equations directly
because of lack of the smoothness. Moreover, new bases of reproducing kernel
spaces are constructed. On the other hand, the existence of any ε-approximate
solution is proved and an effective method for obtaining the ε-approximate
solution is established. A numerical example is given to show the accuracy
and effectiveness of theoretical results. |
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| ISSN: | 0354-9836 2334-7163 |