Normalized Bernstein polynomials in solving space-time fractional diffusion equation
Abstract In this paper, we solve a time-space fractional diffusion equation. Our methods are based on normalized Bernstein polynomials. For the space domain, we use a set of normalized Bernstein polynomials and for the time domain, which is a semi-infinite domain, we offer an algebraic map to make t...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-10-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-017-1401-1 |
| _version_ | 1819076820627095552 |
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| author | A Baseri E Babolian S Abbasbandy |
| author_facet | A Baseri E Babolian S Abbasbandy |
| author_sort | A Baseri |
| collection | DOAJ |
| description | Abstract In this paper, we solve a time-space fractional diffusion equation. Our methods are based on normalized Bernstein polynomials. For the space domain, we use a set of normalized Bernstein polynomials and for the time domain, which is a semi-infinite domain, we offer an algebraic map to make the rational normalized Bernstein functions. This study uses Galerkin and collocation methods. The integrals in the Galerkin method are established with Chebyshev interpolation. We implemented the proposed methods for some examples that are presented to demonstrate the theoretical results. To confirm the accuracy, error analysis is carried out. |
| first_indexed | 2024-12-21T18:47:23Z |
| format | Article |
| id | doaj.art-9eca44140bdd44f092cc0fe1e581c3de |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-21T18:47:23Z |
| publishDate | 2017-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-9eca44140bdd44f092cc0fe1e581c3de2022-12-21T18:53:51ZengSpringerOpenAdvances in Difference Equations1687-18472017-10-012017112510.1186/s13662-017-1401-1Normalized Bernstein polynomials in solving space-time fractional diffusion equationA Baseri0E Babolian1S Abbasbandy2Department of Mathematics, Science and Research Branch, Islamic Azad UniversityDepartment of Mathematics, Science and Research Branch, Islamic Azad UniversityDepartment of Mathematics, Science and Research Branch, Islamic Azad UniversityAbstract In this paper, we solve a time-space fractional diffusion equation. Our methods are based on normalized Bernstein polynomials. For the space domain, we use a set of normalized Bernstein polynomials and for the time domain, which is a semi-infinite domain, we offer an algebraic map to make the rational normalized Bernstein functions. This study uses Galerkin and collocation methods. The integrals in the Galerkin method are established with Chebyshev interpolation. We implemented the proposed methods for some examples that are presented to demonstrate the theoretical results. To confirm the accuracy, error analysis is carried out.http://link.springer.com/article/10.1186/s13662-017-1401-1rational normalized Bernstein functions (RNBF)normalized Bernstein polynomials (NBP)time-space fractional diffusion equationerror analysiscollocation and Galerkin methods |
| spellingShingle | A Baseri E Babolian S Abbasbandy Normalized Bernstein polynomials in solving space-time fractional diffusion equation Advances in Difference Equations rational normalized Bernstein functions (RNBF) normalized Bernstein polynomials (NBP) time-space fractional diffusion equation error analysis collocation and Galerkin methods |
| title | Normalized Bernstein polynomials in solving space-time fractional diffusion equation |
| title_full | Normalized Bernstein polynomials in solving space-time fractional diffusion equation |
| title_fullStr | Normalized Bernstein polynomials in solving space-time fractional diffusion equation |
| title_full_unstemmed | Normalized Bernstein polynomials in solving space-time fractional diffusion equation |
| title_short | Normalized Bernstein polynomials in solving space-time fractional diffusion equation |
| title_sort | normalized bernstein polynomials in solving space time fractional diffusion equation |
| topic | rational normalized Bernstein functions (RNBF) normalized Bernstein polynomials (NBP) time-space fractional diffusion equation error analysis collocation and Galerkin methods |
| url | http://link.springer.com/article/10.1186/s13662-017-1401-1 |
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