Numerical Algorithms for the Fractional Diffusion-Wave Equation with Reaction Term
Two numerical algorithms are derived to compute the fractional diffusion-wave equation with a reaction term. Firstly, using the relations between Caputo and Riemann-Liouville derivatives, we get two equivalent forms of the original equation, where we approximate Riemann-Liouville derivative by a sec...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/493406 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832556570263683072 |
|---|---|
| author | Hengfei Ding Changpin Li |
| author_facet | Hengfei Ding Changpin Li |
| author_sort | Hengfei Ding |
| collection | DOAJ |
| description | Two numerical algorithms are derived to compute the fractional diffusion-wave equation with a reaction term. Firstly, using the relations between Caputo and Riemann-Liouville derivatives, we get two equivalent forms of the original equation, where we approximate Riemann-Liouville derivative by a second-order difference scheme. Secondly, for second-order derivative in space dimension, we construct a fourth-order difference scheme in terms of the hyperbolic-trigonometric spline function. The stability analysis of the derived numerical methods is given by means of the fractional Fourier method. Finally, an illustrative example is presented to show that the numerical results are in good agreement with the theoretical analysis. |
| format | Article |
| id | doaj-art-b7c7da22ea404c1d9df48fd32feac9bc |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-b7c7da22ea404c1d9df48fd32feac9bc2025-02-03T05:44:57ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/493406493406Numerical Algorithms for the Fractional Diffusion-Wave Equation with Reaction TermHengfei Ding0Changpin Li1Department of Mathematics, Shanghai University, Shanghai 200444, ChinaDepartment of Mathematics, Shanghai University, Shanghai 200444, ChinaTwo numerical algorithms are derived to compute the fractional diffusion-wave equation with a reaction term. Firstly, using the relations between Caputo and Riemann-Liouville derivatives, we get two equivalent forms of the original equation, where we approximate Riemann-Liouville derivative by a second-order difference scheme. Secondly, for second-order derivative in space dimension, we construct a fourth-order difference scheme in terms of the hyperbolic-trigonometric spline function. The stability analysis of the derived numerical methods is given by means of the fractional Fourier method. Finally, an illustrative example is presented to show that the numerical results are in good agreement with the theoretical analysis.http://dx.doi.org/10.1155/2013/493406 |
| spellingShingle | Hengfei Ding Changpin Li Numerical Algorithms for the Fractional Diffusion-Wave Equation with Reaction Term Abstract and Applied Analysis |
| title | Numerical Algorithms for the Fractional Diffusion-Wave Equation with Reaction Term |
| title_full | Numerical Algorithms for the Fractional Diffusion-Wave Equation with Reaction Term |
| title_fullStr | Numerical Algorithms for the Fractional Diffusion-Wave Equation with Reaction Term |
| title_full_unstemmed | Numerical Algorithms for the Fractional Diffusion-Wave Equation with Reaction Term |
| title_short | Numerical Algorithms for the Fractional Diffusion-Wave Equation with Reaction Term |
| title_sort | numerical algorithms for the fractional diffusion wave equation with reaction term |
| url | http://dx.doi.org/10.1155/2013/493406 |
| work_keys_str_mv | AT hengfeiding numericalalgorithmsforthefractionaldiffusionwaveequationwithreactionterm AT changpinli numericalalgorithmsforthefractionaldiffusionwaveequationwithreactionterm |