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...
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VINCA Institute of Nuclear Sciences
2016-01-01
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| Series: | Thermal Science |
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| Online Access: | http://www.doiserbia.nb.rs/img/doi/0354-9836/2016/0354-983616701J .pdf |
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doaj-3262383896e24fe89d98c13be092f8292021-01-02T02:24:19ZengVINCA Institute of Nuclear SciencesThermal Science0354-98362334-71632016-01-0120suppl. 370171010.2298/TSCI16S3701J0354-983616701JA new numerical method for solving two-dimensional variable-order anomalous sub-diffusion equationJiang Wei0Guo Beibei1Harbin Institute of Technology at Weihai, Department of Mathematics, Shandong, ChinaHarbin Institute of Technology at Weihai, Department of Mathematics, Shandong, ChinaThe 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.http://www.doiserbia.nb.rs/img/doi/0354-9836/2016/0354-983616701J .pdfvariable-order anomalous sub-diffusion equationsplinereproducing kernel theoryapproximate solution |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Jiang Wei Guo Beibei |
| spellingShingle |
Jiang Wei Guo Beibei A new numerical method for solving two-dimensional variable-order anomalous sub-diffusion equation Thermal Science variable-order anomalous sub-diffusion equation spline reproducing kernel theory approximate solution |
| author_facet |
Jiang Wei Guo Beibei |
| author_sort |
Jiang Wei |
| title |
A new numerical method for solving two-dimensional variable-order anomalous sub-diffusion equation |
| title_short |
A new numerical method for solving two-dimensional variable-order anomalous sub-diffusion equation |
| title_full |
A new numerical method for solving two-dimensional variable-order anomalous sub-diffusion equation |
| title_fullStr |
A new numerical method for solving two-dimensional variable-order anomalous sub-diffusion equation |
| title_full_unstemmed |
A new numerical method for solving two-dimensional variable-order anomalous sub-diffusion equation |
| title_sort |
new numerical method for solving two-dimensional variable-order anomalous sub-diffusion equation |
| publisher |
VINCA Institute of Nuclear Sciences |
| series |
Thermal Science |
| issn |
0354-9836 2334-7163 |
| publishDate |
2016-01-01 |
| description |
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. |
| topic |
variable-order anomalous sub-diffusion equation spline reproducing kernel theory approximate solution |
| url |
http://www.doiserbia.nb.rs/img/doi/0354-9836/2016/0354-983616701J .pdf |
| work_keys_str_mv |
AT jiangwei anewnumericalmethodforsolvingtwodimensionalvariableorderanomaloussubdiffusionequation AT guobeibei anewnumericalmethodforsolvingtwodimensionalvariableorderanomaloussubdiffusionequation AT jiangwei newnumericalmethodforsolvingtwodimensionalvariableorderanomaloussubdiffusionequation AT guobeibei newnumericalmethodforsolvingtwodimensionalvariableorderanomaloussubdiffusionequation |
| _version_ |
1724361993995943936 |