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 inNonlinear engineering Vol. 7; no. 2; pp. 113 - 125
Main Authors Singh, Brajesh Kumar, Kumar, Pramod
Format Journal Article
LanguageEnglish
Published Berlin De Gruyter 26.06.2018
Walter de Gruyter GmbH
Subjects
Online AccessGet full text
ISSN2192-8010
2192-8029
2192-8029
DOI10.1515/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
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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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References (ref221) 2016; 24
(ref01) 2010; 60
(ref291) 2016; 274
(ref101) 2012; 35
(ref341) 1983
(ref51) 2009; 25
(ref211) 2016; 10
(ref31) 2010; 34
(ref121) 2009; 230
(ref361) 1975
(ref111) 2016; 55
(ref41) 2011; 24
ref351
(ref261) 2011; 11
(ref321) 2015; 13
(ref71) 2011; 348
(ref131) 2009; 25
(ref141) 1972; 10
(ref181) 2013; 38
(ref251) 1992; 15
(ref151) 1989; 13
(ref241) 2011; 28
(ref81) 2014; 244
(ref171) 2013; 30
(ref311) 2002; 40
(ref271) 2015; 42
(ref191) 2013; 224
(ref231) 1995; 111
(ref331) 2016
(ref91) 2001; 17
(ref61) 2012; 218
(ref201) 2016; 3
(ref21) 1990
(ref301) 2015; 16
(ref11) 2010; 34
(ref161) 1989; 13
(ref281) 2015; 12
References_xml – volume: 10
  start-page: 40
  year: 1972
  ident: ref141
  article-title: Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations
  publication-title: J. Comput. Phys.
  doi: 10.1016/0021-9991(72)90089-7
– volume-title: Numerical Solution of Differential Equations
  year: 1983
  ident: ref341
– volume: 25
  start-page: 494
  year: 2009
  ident: ref131
  article-title: A meshless method for numerical solution of a linear hyperbolic equation with variable coefficients in two space dimensions
  publication-title: Numer. Methods Partial Differ. Equ.
  doi: 10.1002/num.20357
– volume: 3
  start-page: 1261527
  year: 2016
  ident: ref201
  article-title: A novel approach for numeric study of 2D biological population model
  publication-title: Cogent Mathematics
  doi: 10.1080/23311835.2016.1261527
– volume: 10
  start-page: 1
  year: 2016
  ident: ref211
  article-title: A new numerical approach for the solutions of partial differential equations in three-dimensional space
  publication-title: Appl. Math. Inf. Sci.
– volume: 30
  start-page: 320
  year: 2013
  ident: ref171
  article-title: Cubic B-spline differential quadrature methods and stability for Burgers’ equation
  publication-title: Eng. Comput. Int. J. Comput. Aided Eng. Software
– year: 2016
  ident: ref331
  article-title: A novel aproach for numerical study of two dimensional hyperbolic telegraph equation
  publication-title: Alexandria Eng. J.
– volume: 16
  year: 2015
  ident: ref301
  article-title: Numerical simulations for transport of conservative pollutants
  publication-title: Selcuk J. Appl. Math.
– volume: 13
  start-page: 1017
  year: 1989
  ident: ref151
  article-title: New insights in solving distributed system equations by the quadrature method-II
  publication-title: Comput. Chem. Eng.
  doi: 10.1016/0098-1354(89)87043-7
– volume: 24
  start-page: 629
  year: 2016
  ident: ref221
  article-title: A numerical scheme for the generalized Burgers-Huxley equation
  publication-title: Journal of the Egyptian Mathematical Society
  doi: 10.1016/j.joems.2015.11.003
– volume: 348
  start-page: 2863
  year: 2011
  ident: ref71
  article-title: Polynomial based differential quadrature method for numerical solution of nonlinear Burgers’ equation
  publication-title: J. Franklin Inst.
  doi: 10.1016/j.jfranklin.2011.09.008
– volume: 25
  start-page: 232
  year: 2009
  ident: ref51
  article-title: High order implicit collocation method for the solution of two-dimensional linear hyperbolic equation
  publication-title: Numer. Methods Partial Differ. Equ.
  doi: 10.1002/num.20341
– volume: 15
  start-page: 791
  year: 1992
  ident: ref251
  article-title: Application of generalized differential quadrature to solve two dimensional incompressible navier-Stokes equations
  publication-title: Int. J. Numer. Meth. Fluids
  doi: 10.1002/fld.1650150704
– volume: 224
  start-page: 166
  year: 2013
  ident: ref191
  article-title: Numerical solution of Burgers’ equation with modified cubic B-spline differential quadrature method
  publication-title: Applied Math. Comput.
– volume: 34
  start-page: 51
  year: 2010
  ident: ref31
  article-title: Solution of the second-order one-dimensional hyperbolic telegraph equation by using the dual reciprocity boundary integral equation (DRBIE) method
  publication-title: Eng. Anal. Bound. Elem.
  doi: 10.1016/j.enganabound.2009.07.002
– volume: 13
  start-page: 779
  year: 1989
  ident: ref161
  article-title: New insights in solving distributed system equations by the quadrature method-I
  publication-title: Comput. Chem. Eng.
  doi: 10.1016/0098-1354(89)85051-3
– volume: 218
  start-page: 7279
  year: 2012
  ident: ref61
  article-title: A differential quadrature algorithm to solve the two dimensional linear hyperbolic telegraph equation with Dirichlet and Neumann boundary conditions
  publication-title: Appl. Math. Comput.
– volume: 12
  start-page: 113
  year: 2015
  ident: ref281
  article-title: B-spline differential quadrature method for modified Burgers equation
  publication-title: Çankaya Univ. J. Sci. Engg.
– volume: 60
  start-page: 1964
  year: 2010
  ident: ref01
  article-title: Numerical solution of telegraph equation using interpolating scaling functions
  publication-title: Comput. Math. Appl.
  doi: 10.1016/j.camwa.2010.07.030
– volume: 28
  start-page: 654
  year: 2011
  ident: ref241
  article-title: Shock wave simulations using sinc differential quadrature method
  publication-title: Eng. Comput. Int. J. Comput. Aided Eng. Software
– volume: 230
  start-page: 626
  year: 2009
  ident: ref121
  article-title: A new fourth-order compact finite difference scheme for the two-dimensional second-order hyperbolic equation
  publication-title: J. Comput. Appl. Math.
  doi: 10.1016/j.cam.2009.01.001
– volume: 40
  start-page: 469
  year: 2002
  ident: ref311
  article-title: A new class of optimal high-order strong stability-preserving time-stepping schemes
  publication-title: SIAM J. Numer.Analysis
  doi: 10.1137/S0036142901389025
– volume: 274
  start-page: 208
  year: 2016
  ident: ref291
  article-title: Quartic and quintic Bspline methods for advection diffusion equation
  publication-title: Applied Mathematics and Computation
  doi: 10.1016/j.amc.2015.11.004
– volume: 11
  start-page: 403
  year: 2011
  ident: ref261
  article-title: Quartic B-spline differential quadrature method
  publication-title: Int. J. Nonlinear Sci.
– volume: 24
  start-page: 1716
  year: 2011
  ident: ref41
  article-title: A Taylor matrix method for the solution of a two-dimensional linear hyperbolic equation
  publication-title: Appl. Math. Lett.
  doi: 10.1016/j.aml.2011.04.026
– volume: 111
  start-page: 85
  year: 1995
  ident: ref231
  article-title: Harmonic differential quadrature method and applications to analysis of structural components
  publication-title: Acta Mech.
  doi: 10.1007/BF01187729
– volume: 244
  start-page: 976
  year: 2014
  ident: ref81
  article-title: A numerical study of two dimensional hyperbolic telegraph equation by modified B-spline differential quadrature method
  publication-title: Appl. Math. Comput.
– volume: 34
  start-page: 324
  year: 2010
  ident: ref11
  article-title: Combination of meshless local weak and strong (MLWS) forms to solve the two dimensional hyperbolic telegraph equation
  publication-title: Eng. Anal. Bound. Elem.
  doi: 10.1016/j.enganabound.2009.10.010
– volume: 42
  start-page: 67
  year: 2015
  ident: ref271
  article-title: Approximation of the KdVB equation by the quintic B-spline differential quadrature method
  publication-title: Kuwait J. Sci.
– volume: 17
  start-page: 684
  year: 2001
  ident: ref91
  article-title: An unconditionally stable alternating direction implicit scheme for the two space dimensional linear hyperbolic equation
  publication-title: Numer. Methods Partial Differ. Equ.
  doi: 10.1002/num.1034
– volume: 13
  start-page: 414
  year: 2015
  ident: ref321
  article-title: Numerical solutions of the reaction diffusion system by using exponential cubic B-spline collocation algorithms
  publication-title: Open Phys.
– volume-title: Microwave Engineering
  year: 1990
  ident: ref21
– volume-title: Splines and Variational Methods
  year: 1975
  ident: ref361
– volume: 38
  start-page: 1151
  year: 2013
  ident: ref181
  article-title: Numerical simulations of boundary - forced RLW equation with cubic B-spline-based differential quadrature methods
  publication-title: Arab J Sci Eng
  doi: 10.1007/s13369-012-0353-8
– volume: 55
  start-page: 3331
  year: 2016
  ident: ref111
  article-title: A novel approach for numerical computation of Burgers equation (1 + 1) and (2 + 1) dimension
  publication-title: Alexandria Eng. J.
  doi: 10.1016/j.aej.2016.08.023
– ident: ref351
  publication-title: Optimal strong-stability-preserving Runge-Kutta time discretizations for discontinuous Galerkin methods
– volume: 35
  start-page: 1220
  year: 2012
  ident: ref101
  article-title: A method based on meshless approach for the numerical solution of the two-space dimensional hyperbolic telegraph equation
  publication-title: Math. Methods Appl. Sci.
  doi: 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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