An algorithm based on a new DQM with modified extended cubic B-splines for numerical study of two dimensional hyperbolic telegraph equation
In this paper, a new approach “modified extended cubic B-Spline differential quadrature (mECDQ) method” has been developed for the numerical computation of two dimensional hyperbolic telegraph equation. The mECDQ method is a DQM based on modified extended cubic B-spline functions as new base functio...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2018-03-01
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| Series: | Alexandria Engineering Journal |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016816303076 |
| _version_ | 1819107537757143040 |
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| author | Brajesh Kumar Singh Pramod Kumar |
| author_facet | Brajesh Kumar Singh Pramod Kumar |
| author_sort | Brajesh Kumar Singh |
| collection | DOAJ |
| description | In this paper, a new approach “modified extended cubic B-Spline differential quadrature (mECDQ) method” has been developed for the numerical computation of two dimensional hyperbolic telegraph equation. The mECDQ method is a DQM based on modified extended cubic B-spline functions as new base functions. The mECDQ method reduces the hyperbolic telegraph equation into an amenable system of ordinary differential equations (ODEs), in time. The resulting system of ODEs has been solved by adopting an optimal five stage fourth-order strong stability preserving Runge - Kutta (SSP-RK54) scheme. The stability of the method is also studied by computing the eigenvalues of the coefficient matrices. It is shown that the mECDQ method produces stable solution for the telegraph equation. The accuracy of the method is illustrated by computing the errors between analytical solutions and numerical solutions are measured in terms of L2 and L∞ and average error norms for each problem. A comparison of mECDQ solutions with the results of the other numerical methods has been carried out for various space sizes and time step sizes, which shows that the mECDQ solutions are converging very fast in comparison with the various existing schemes. Keywords: Differential quadrature method, Hyperbolic telegraph equation, Modified extended cubic B-splines, mECDQ method, Thomas algorithm |
| first_indexed | 2024-12-22T02:55:37Z |
| format | Article |
| id | doaj.art-acffe344206b4a9ca7063ec15ad056b3 |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-12-22T02:55:37Z |
| publishDate | 2018-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-acffe344206b4a9ca7063ec15ad056b32022-12-21T18:41:16ZengElsevierAlexandria Engineering Journal1110-01682018-03-01571175191An algorithm based on a new DQM with modified extended cubic B-splines for numerical study of two dimensional hyperbolic telegraph equationBrajesh Kumar Singh0Pramod Kumar1Corresponding author.; Department of Applied Mathematics, School for Physical Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow 226 025, UP, IndiaDepartment of Applied Mathematics, School for Physical Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow 226 025, UP, IndiaIn this paper, a new approach “modified extended cubic B-Spline differential quadrature (mECDQ) method” has been developed for the numerical computation of two dimensional hyperbolic telegraph equation. The mECDQ method is a DQM based on modified extended cubic B-spline functions as new base functions. The mECDQ method reduces the hyperbolic telegraph equation into an amenable system of ordinary differential equations (ODEs), in time. The resulting system of ODEs has been solved by adopting an optimal five stage fourth-order strong stability preserving Runge - Kutta (SSP-RK54) scheme. The stability of the method is also studied by computing the eigenvalues of the coefficient matrices. It is shown that the mECDQ method produces stable solution for the telegraph equation. The accuracy of the method is illustrated by computing the errors between analytical solutions and numerical solutions are measured in terms of L2 and L∞ and average error norms for each problem. A comparison of mECDQ solutions with the results of the other numerical methods has been carried out for various space sizes and time step sizes, which shows that the mECDQ solutions are converging very fast in comparison with the various existing schemes. Keywords: Differential quadrature method, Hyperbolic telegraph equation, Modified extended cubic B-splines, mECDQ method, Thomas algorithmhttp://www.sciencedirect.com/science/article/pii/S1110016816303076 |
| spellingShingle | Brajesh Kumar Singh Pramod Kumar An algorithm based on a new DQM with modified extended cubic B-splines for numerical study of two dimensional hyperbolic telegraph equation Alexandria Engineering Journal |
| title | An algorithm based on a new DQM with modified extended cubic B-splines for numerical study of two dimensional hyperbolic telegraph equation |
| title_full | An algorithm based on a new DQM with modified extended cubic B-splines for numerical study of two dimensional hyperbolic telegraph equation |
| title_fullStr | An algorithm based on a new DQM with modified extended cubic B-splines for numerical study of two dimensional hyperbolic telegraph equation |
| title_full_unstemmed | An algorithm based on a new DQM with modified extended cubic B-splines for numerical study of two dimensional hyperbolic telegraph equation |
| title_short | An algorithm based on a new DQM with modified extended cubic B-splines for numerical study of two dimensional hyperbolic telegraph equation |
| title_sort | algorithm based on a new dqm with modified extended cubic b splines for numerical study of two dimensional hyperbolic telegraph equation |
| url | http://www.sciencedirect.com/science/article/pii/S1110016816303076 |
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