An algorithm based on a new DQM with modified exponential cubic B-splines for solving hyperbolic telegraph equation in (2 + 1) dimension
In this paper, a new method (mExp-DQM) has been developed for space discretization together with a time integration algorithm for numeric study of (2 + 1) dimensional hyperbolic telegraph equations. The mExp-DQM (i.e., differential quadrature method with modified exponential cubic B-splines as new b...
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| Published in | Nonlinear engineering Vol. 7; no. 2; pp. 113 - 125 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin
De Gruyter
26.06.2018
Walter de Gruyter GmbH |
| Subjects | |
| Online Access | Get full text |
| ISSN | 2192-8010 2192-8029 2192-8029 |
| DOI | 10.1515/nleng-2017-0106 |
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| Abstract | In this paper, a new method
(mExp-DQM) has been developed for space discretization together with a time integration algorithm for numeric study of (2 + 1) dimensional hyperbolic telegraph equations. The mExp-DQM (i.e., differential quadrature method with modified exponential cubic B-splines as new basis) reduces the problem into an amenable system of ordinary differential equations (ODEs), in time. The time integration SSP-RK54 algorithm has been adopted to solve the resulting system of ODEs. The proposed method is shown stable by computing the eigenvalues of the coefficients matrices while the accuracy of the method is illustrated in terms of
and
error norms for each problem. A comparison of mExp-DQM solutions with the results of the other numerical methods has been carried out for various space sizes and time step sizes. |
|---|---|
| AbstractList | In this paper, a new method [modified exponential cubic B]-[Spline differential quadrature method] (mExp-DQM) has been developed for space discretization together with a time integration algorithm for numeric study of (2 + 1) dimensional hyperbolic telegraph equations. The mExp-DQM (i.e., differential quadrature method with modified exponential cubic B-splines as new basis) reduces the problem into an amenable system of ordinary differential equations (ODEs), in time. The time integration SSP-RK54 algorithm has been adopted to solve the resulting system of ODEs. The proposed method is shown stable by computing the eigenvalues of the coefficients matrices while the accuracy of the method is illustrated in terms of [L][2] and [L][∞] error norms for each problem. A comparison of mExp-DQM solutions with the results of the other numerical methods has been carried out for various space sizes and time step sizes. In this paper, a new method modified exponential cubic B-Spline differential quadrature method (mExp-DQM) has been developed for space discretization together with a time integration algorithm for numeric study of (2 + 1) dimensional hyperbolic telegraph equations. The mExp-DQM (i.e., differential quadrature method with modified exponential cubic B-splines as new basis) reduces the problem into an amenable system of ordinary differential equations (ODEs), in time. The time integration SSP-RK54 algorithm has been adopted to solve the resulting system of ODEs. The proposed method is shown stable by computing the eigenvalues of the coefficients matrices while the accuracy of the method is illustrated in terms of L2 and L∞ error norms for each problem. A comparison of mExp-DQM solutions with the results of the other numerical methods has been carried out for various space sizes and time step sizes. In this paper, a new method (mExp-DQM) has been developed for space discretization together with a time integration algorithm for numeric study of (2 + 1) dimensional hyperbolic telegraph equations. The mExp-DQM (i.e., differential quadrature method with modified exponential cubic B-splines as new basis) reduces the problem into an amenable system of ordinary differential equations (ODEs), in time. The time integration SSP-RK54 algorithm has been adopted to solve the resulting system of ODEs. The proposed method is shown stable by computing the eigenvalues of the coefficients matrices while the accuracy of the method is illustrated in terms of and error norms for each problem. A comparison of mExp-DQM solutions with the results of the other numerical methods has been carried out for various space sizes and time step sizes. In this paper, a new method modified exponential cubic B - Spline differential quadrature method (mExp-DQM) has been developed for space discretization together with a time integration algorithm for numeric study of (2 + 1) dimensional hyperbolic telegraph equations. The mExp-DQM (i.e., differential quadrature method with modified exponential cubic B-splines as new basis) reduces the problem into an amenable system of ordinary differential equations (ODEs), in time. The time integration SSP-RK54 algorithm has been adopted to solve the resulting system of ODEs. The proposed method is shown stable by computing the eigenvalues of the coefficients matrices while the accuracy of the method is illustrated in terms of L 2 and L ∞ error norms for each problem. A comparison of mExp-DQM solutions with the results of the other numerical methods has been carried out for various space sizes and time step sizes. |
| Author | Kumar, Pramod Singh, Brajesh Kumar |
| Author_xml | – sequence: 1 givenname: Brajesh Kumar surname: Singh fullname: Singh, Brajesh Kumar organization: Department of Applied Mathematics, Babasaheb Bhimrao Ambedkar University, Lucknow, 226 025 (UP), India – sequence: 2 givenname: Pramod surname: Kumar fullname: Kumar, Pramod organization: Department of Applied Mathematics, School for Physical Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow, 226 025 (UP), India |
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| Cites_doi | 10.1016/0021-9991(72)90089-7 10.1002/num.20357 10.1080/23311835.2016.1261527 10.1016/0098-1354(89)87043-7 10.1016/j.joems.2015.11.003 10.1016/j.jfranklin.2011.09.008 10.1002/num.20341 10.1002/fld.1650150704 10.1016/j.enganabound.2009.07.002 10.1016/0098-1354(89)85051-3 10.1016/j.camwa.2010.07.030 10.1016/j.cam.2009.01.001 10.1137/S0036142901389025 10.1016/j.amc.2015.11.004 10.1016/j.aml.2011.04.026 10.1007/BF01187729 10.1016/j.enganabound.2009.10.010 10.1002/num.1034 10.1007/s13369-012-0353-8 10.1016/j.aej.2016.08.023 10.1002/mma.2517 |
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| Snippet | In this paper, a new method
(mExp-DQM) has been developed for space discretization together with a time integration algorithm for numeric study of (2 + 1)... In this paper, a new method modified exponential cubic B - Spline differential quadrature method (mExp-DQM) has been developed for space discretization... In this paper, a new method [modified exponential cubic B]-[Spline differential quadrature method] (mExp-DQM) has been developed for space discretization... In this paper, a new method modified exponential cubic B-Spline differential quadrature method (mExp-DQM) has been developed for space discretization together... |
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| SubjectTerms | 35L04 35L10 74Sxx Algorithms Differential equations Differential quadrature method Eigenvalues hyperbolic telegraph equation mExp-DQM modified exponential cubic B-splines Norms Numerical methods Ordinary differential equations Splines Thomas algorithm Time integration |
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| Title | An algorithm based on a new DQM with modified exponential cubic B-splines for solving hyperbolic telegraph equation in (2 + 1) dimension |
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