Numerical solution of fractional diffusion wave equation and fractional klein–gordon equation via two-dimensional genocchi polynomials with a ritz–galerkin method
In this paper, two-dimensional Genocchi polynomials and the Ritz–Galerkin method were developed to investigate the Fractional Diffusion Wave Equation (FDWE) and the Fractional Klein–Gordon Equation (FKGE). A satisfier function that satisfies all the initial and boundary conditions was used. A linear...
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2018
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| Online Access: | http://eprints.uthm.edu.my/5744/1/AJ%202018%20%28341%29.pdf http://eprints.uthm.edu.my/5744/ |
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| author | Kanwal, Afshan Chang, Phang Iqbal, Umer |
| author_facet | Kanwal, Afshan Chang, Phang Iqbal, Umer |
| author_sort | Kanwal, Afshan |
| building | UTHM Library |
| collection | Institutional Repository |
| content_provider | Universiti Tun Hussein Onn Malaysia |
| content_source | UTHM Institutional Repository |
| continent | Asia |
| country | Malaysia |
| description | In this paper, two-dimensional Genocchi polynomials and the Ritz–Galerkin method were developed to investigate the Fractional Diffusion Wave Equation (FDWE) and the Fractional Klein–Gordon Equation (FKGE). A satisfier function that satisfies all the initial and boundary conditions was used. A linear system of algebraic equations was obtained for the considered equation with the help of two-dimensional Genocchi polynomials along with the Ritz–Galerkin method. The FDWE and FKGE, including the nonlinear case, were reduced to solve the linear system of the algebraic equation. Hence, the proposed method was able to greatly reduce the complexity of the problems and provide an accurate solution. The effectiveness of the proposed technique is demonstrated through several examples. |
| format | Article |
| id | my.uthm.eprints-5744 |
| institution | Universiti Tun Hussein Onn Malaysia |
| language | en |
| publishDate | 2018 |
| publisher | MDPI |
| record_format | eprints |
| spelling | my.uthm.eprints-57442022-01-23T03:16:26Z http://eprints.uthm.edu.my/5744/ Numerical solution of fractional diffusion wave equation and fractional klein–gordon equation via two-dimensional genocchi polynomials with a ritz–galerkin method Kanwal, Afshan Chang, Phang Iqbal, Umer QA Mathematics QA1-43 General QA150-272.5 Algebra In this paper, two-dimensional Genocchi polynomials and the Ritz–Galerkin method were developed to investigate the Fractional Diffusion Wave Equation (FDWE) and the Fractional Klein–Gordon Equation (FKGE). A satisfier function that satisfies all the initial and boundary conditions was used. A linear system of algebraic equations was obtained for the considered equation with the help of two-dimensional Genocchi polynomials along with the Ritz–Galerkin method. The FDWE and FKGE, including the nonlinear case, were reduced to solve the linear system of the algebraic equation. Hence, the proposed method was able to greatly reduce the complexity of the problems and provide an accurate solution. The effectiveness of the proposed technique is demonstrated through several examples. MDPI 2018 Article PeerReviewed text en http://eprints.uthm.edu.my/5744/1/AJ%202018%20%28341%29.pdf Kanwal, Afshan and Chang, Phang and Iqbal, Umer (2018) Numerical solution of fractional diffusion wave equation and fractional klein–gordon equation via two-dimensional genocchi polynomials with a ritz–galerkin method. Computation, 6 (3). pp. 1-12. ISSN 2079-3197 |
| spellingShingle | QA Mathematics QA1-43 General QA150-272.5 Algebra Kanwal, Afshan Chang, Phang Iqbal, Umer Numerical solution of fractional diffusion wave equation and fractional klein–gordon equation via two-dimensional genocchi polynomials with a ritz–galerkin method |
| title | Numerical solution of fractional diffusion wave equation and fractional klein–gordon equation via two-dimensional genocchi polynomials with a ritz–galerkin method |
| title_full | Numerical solution of fractional diffusion wave equation and fractional klein–gordon equation via two-dimensional genocchi polynomials with a ritz–galerkin method |
| title_fullStr | Numerical solution of fractional diffusion wave equation and fractional klein–gordon equation via two-dimensional genocchi polynomials with a ritz–galerkin method |
| title_full_unstemmed | Numerical solution of fractional diffusion wave equation and fractional klein–gordon equation via two-dimensional genocchi polynomials with a ritz–galerkin method |
| title_short | Numerical solution of fractional diffusion wave equation and fractional klein–gordon equation via two-dimensional genocchi polynomials with a ritz–galerkin method |
| title_sort | numerical solution of fractional diffusion wave equation and fractional klein–gordon equation via two-dimensional genocchi polynomials with a ritz–galerkin method |
| topic | QA Mathematics QA1-43 General QA150-272.5 Algebra |
| url | http://eprints.uthm.edu.my/5744/1/AJ%202018%20%28341%29.pdf http://eprints.uthm.edu.my/5744/ |
| url_provider | http://eprints.uthm.edu.my/ |