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Volumn 218, Issue 15, 2012, Pages 7839-7855

Numerical solutions of nonlinear Burgers' equation with modified cubic B-splines collocation method

Author keywords

Modified cubic B splines basis functions; Nonlinear Burgers' equation; SSP RK43 scheme; SSP RK54 scheme; Thomas algorithm

Indexed keywords

BASIS FUNCTIONS; NONLINEAR BURGERS' EQUATION; SSP-RK43 SCHEME; SSP-RK54 SCHEME; THOMAS ALGORITHM;

EID: 84858333742     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2012.01.059     Document Type: Article
Times cited : (207)

References (29)
  • 1
    • 77953133901 scopus 로고    scopus 로고
    • Numerical solution of the Burgers' equation by automatic differentiation
    • Asai Asaithambi Numerical solution of the Burgers' equation by automatic differentiation Appl. Math. Comput. 216 2010 2700 2708
    • (2010) Appl. Math. Comput. , vol.216 , pp. 2700-2708
    • Asaithambi, A.1
  • 2
    • 4444378330 scopus 로고    scopus 로고
    • Finite element approach to Burgers' equation
    • Abdulkadir Dogan, and A. Galerkin Finite element approach to Burgers' equation Appl. Math. Comput. 157 2004 331 346
    • (2004) Appl. Math. Comput. , vol.157 , pp. 331-346
    • Dogan, A.1    Galerkin, A.2
  • 4
    • 53449090789 scopus 로고    scopus 로고
    • A Chebyshev spectral collocation method for solving Burgers' type equations
    • A.H. Khater, R.S. Temsah, and M.M. Hassan A Chebyshev spectral collocation method for solving Burgers' type equations J. Comput. Appl. Math. 222 2008 333 350
    • (2008) J. Comput. Appl. Math. , vol.222 , pp. 333-350
    • Khater, A.H.1    Temsah, R.S.2    Hassan, M.M.3
  • 5
    • 80052213097 scopus 로고    scopus 로고
    • Shock wave simulations using Sinc Differential Quadrature Method
    • Alper Korkmaz Shock wave simulations using Sinc Differential Quadrature Method Int. J. Comput. Aided Eng. Software 28 6 2011 654 674
    • (2011) Int. J. Comput. Aided Eng. Software , vol.28 , Issue.6 , pp. 654-674
    • Korkmaz, A.1
  • 6
    • 80255123668 scopus 로고    scopus 로고
    • Polynomial based differential quadrature method for numerical solution of nonlinear Burgers' equation
    • 10.1016/j.jfranklin.2011.09.008
    • Alper Korkmaz, and Idris Daǧ Polynomial based differential quadrature method for numerical solution of nonlinear Burgers' equation J. Franklin Inst. 2011 10.1016/j.jfranklin.2011.09.008
    • (2011) J. Franklin Inst.
    • Korkmaz, A.1    Daǧ, I.2
  • 7
    • 84858334328 scopus 로고    scopus 로고
    • Quartic B-spline Differential Quadrature Method
    • Alper Korkmaz, A. Murat Aksoy, and Idris Dag Quartic B-spline Differential Quadrature Method Int. J. Nonlinear Sci. 11 4 2011 403 411
    • (2011) Int. J. Nonlinear Sci. , vol.11 , Issue.4 , pp. 403-411
    • Korkmaz, A.1    Murat Aksoy, A.2    Dag, I.3
  • 8
    • 79960752482 scopus 로고    scopus 로고
    • Some numerical methods for solving Burgers equation
    • A.K. Khalifa, Khalida Inayat Noor, and Muhammad Aslam Noor Some numerical methods for solving Burgers equation Int. J. Phys. Sci. 6 7 2011 1702 1710
    • (2011) Int. J. Phys. Sci. , vol.6 , Issue.7 , pp. 1702-1710
    • Khalifa, A.K.1    Noor, K.I.2    Noor, M.A.3
  • 9
    • 33845310038 scopus 로고    scopus 로고
    • Quartic B-spline collocation method to the numerical solutions of the Burgers' equation
    • DOI 10.1016/j.chaos.2005.11.037, PII S0960077905011409
    • Bülent Saka, and Idris Dag Quartic B-spline collocation method to the numerical solutions of the Burgers' equation Chaos Solitons Fractals 32 2007 1125 1137 (Pubitemid 44873077)
    • (2007) Chaos, Solitons and Fractals , vol.32 , Issue.3 , pp. 1125-1137
    • Saka, B.1    Dag, I.2
  • 11
    • 33644587866 scopus 로고    scopus 로고
    • Quadratic B-spline finite element method for numerical solution of the Burgers' equation
    • E.N. Aksan Quadratic B-spline finite element method for numerical solution of the Burgers' equation Appl. Math. Comput. 174 2006 884 896
    • (2006) Appl. Math. Comput. , vol.174 , pp. 884-896
    • Aksan, E.N.1
  • 12
    • 79551660746 scopus 로고    scopus 로고
    • Soliton and numerical solutions of the Burgers' Equation and comparing them
    • Esmaeel Hesameddini, and Razieh Gholampour Soliton and numerical solutions of the Burgers' Equation and comparing them Int. J. Math. Anal. 4 52 2010 2547 2564
    • (2010) Int. J. Math. Anal. , vol.4 , Issue.52 , pp. 2547-2564
    • Hesameddini, E.1    Gholampour, R.2
  • 13
    • 78650698074 scopus 로고    scopus 로고
    • Numerical solutions of linear and nonlinear diffusion equations by a differential quadrature method (DQM)
    • G. Güraslan, and M. Sari Numerical solutions of linear and nonlinear diffusion equations by a differential quadrature method (DQM) Int. J. Numer. Methods Biomed. Eng. 27 2011 69 77
    • (2011) Int. J. Numer. Methods Biomed. Eng. , vol.27 , pp. 69-77
    • Güraslan, G.1    Sari, M.2
  • 14
    • 31044432795 scopus 로고    scopus 로고
    • B-spline collocation methods for numerical solutions of the Burgers' equation
    • DOI 10.1155/MPE.2005.521
    • I. Dag, D. Irk, and A. Sahin B-Spline collocation methods for numerical solutions of the Burgers' equation Math. Probl. Eng. 5 2005 521 538 (Pubitemid 43120979)
    • (2005) Mathematical Problems in Engineering , vol.2005 , Issue.5 , pp. 521-538
    • Dag, I.1    Irk, D.2    Sahin, A.3
  • 15
    • 27144455801 scopus 로고    scopus 로고
    • Fourth-order finite difference method for solving Burgers' equation
    • DOI 10.1016/j.amc.2004.12.052, PII S009630030500024X
    • I.A. Hassanien, A.A. Salama, and H.A. Hosham Fourth-order finite difference method for solving Burgers' equation Appl. Math. Comput. 170 2005 781 800 (Pubitemid 41497795)
    • (2005) Applied Mathematics and Computation , vol.170 , Issue.2 , pp. 781-800
    • Hassanien, I.A.1    Salama, A.A.2    Hosham, H.A.3
  • 17
    • 79955703532 scopus 로고    scopus 로고
    • Numerical solution of Burgers' equation with factorized diagonal Padé approximation
    • Kemal Altiparmak Numerical solution of Burgers' equation with factorized diagonal Padé approximation Int. J. Numer. Methods Heat Fluid Flow 21 3 2011 310 319
    • (2011) Int. J. Numer. Methods Heat Fluid Flow , vol.21 , Issue.3 , pp. 310-319
    • Altiparmak, K.1
  • 18
    • 28244479844 scopus 로고    scopus 로고
    • A collocation solution for burgers equation using quadratic B-spline finite elements
    • DOI 10.1080/0020716031000079554
    • K.R. Raslan A collocation solution for Burgers equation using quadratic B-spline finite elements Int. J. Comput. Math. 80 7 2003 931 938 (Pubitemid 41710517)
    • (2003) International Journal of Computer Mathematics , vol.80 , Issue.7 , pp. 931-938
    • Raslan, K.R.1
  • 19
    • 74249110520 scopus 로고    scopus 로고
    • Application of the non-polynomial spline approach to the solution of the Burgers equation
    • M.A. Ramadan, T.S. El-Danaf, and F.E.I. Abd Alaal Application of the non-polynomial spline approach to the solution of the Burgers equation Open Appl. Math. J. 1 2007 15 20
    • (2007) Open Appl. Math. J. , vol.1 , pp. 15-20
    • Ramadan, M.A.1    El-Danaf, T.S.2    Abd Alaal, F.E.I.3
  • 21
    • 78650175080 scopus 로고    scopus 로고
    • A novel numerical scheme for solving Burgers' equation
    • Min Xu, Ren-Hong Wang, Ji-Hong Zhang, and Qin Fang A novel numerical scheme for solving Burgers' equation Appl. Math. Comput. 217 2011 4473 4482
    • (2011) Appl. Math. Comput. , vol.217 , pp. 4473-4482
    • Xu, M.1    Wang, R.-H.2    Zhang, J.-H.3    Fang, Q.4
  • 23
    • 0030363673 scopus 로고    scopus 로고
    • Numerical solution of periodic Burger equation
    • R.C. Mittal, and P. Singhal Numerical solution of periodic Burger equation Ind. J. Pure Appl. Math. 27 7 1996 689 700
    • (1996) Ind. J. Pure Appl. Math. , vol.27 , Issue.7 , pp. 689-700
    • Mittal, R.C.1    Singhal, P.2
  • 24
    • 0039728591 scopus 로고    scopus 로고
    • Numerical solution of the one-dimensional Burgers' equation: Explicit and exact-explicit finite difference methods
    • S. Kutulay, A.R. Bahadir, and A. Özdes Numerical solution of the one-dimensional Burgers' equation: explicit and exact-explicit finite difference methods J. Comput. Appl. Math. 103 1999 251 261
    • (1999) J. Comput. Appl. Math. , vol.103 , pp. 251-261
    • Kutulay, S.1    Bahadir, A.R.2    Özdes, A.3
  • 25
    • 2342444094 scopus 로고    scopus 로고
    • Numerical solutions of the Burgers' equation by the least-squares quadratic B-spline finite element method
    • DOI 10.1016/j.cam.2003.09.043, PII S0377042703008768
    • S. Kutulay, A. Esen, and I. Dag Numerical solutions of the Burgers' equation by the least-squares quadratic B-spline finite element method J. Comput. Appl. Math. 167 2004 21 33 (Pubitemid 38562790)
    • (2004) Journal of Computational and Applied Mathematics , vol.167 , Issue.1 , pp. 21-33
    • Kutluay, S.1    Esen, A.2    Dag, I.3
  • 26
    • 39049173059 scopus 로고    scopus 로고
    • Numerical solution of one-dimensional Burgers' equation using reproducing kernel function
    • DOI 10.1016/j.cam.2007.03.010, PII S0377042707001379
    • Shu-Sen Xie, Sunyeong Heo, Seokchan Kim, Gyungsoo Woo, and Sucheol Yi Numerical solution of one-dimensional Burgers' equation using reproducing kernel function J. Comput. Appl. Math. 214 2008 417 434 (Pubitemid 351241079)
    • (2008) Journal of Computational and Applied Mathematics , vol.214 , Issue.2 , pp. 417-434
    • Xie, S.-S.1    Heo, S.2    Kim, S.3    Woo, G.4    Yi, S.5
  • 27
    • 17444383810 scopus 로고    scopus 로고
    • Numerical solution of Burgers' equation by quadratic B-spline finite elements
    • DOI 10.1016/j.amc.2004.04.101, PII S0096300304003789
    • T. Özis, A. Esen, and S. Kutluay Numerical solution of Burgers' equation by quadratic B-spline finite elements Appl. Math. Comput. 165 2005 237 249 (Pubitemid 40537186)
    • (2005) Applied Mathematics and Computation , vol.165 , Issue.1 , pp. 237-249
    • Ozis, T.1    Esen, A.2    Kutluay, S.3
  • 28
    • 56949103891 scopus 로고    scopus 로고
    • An implicit fourth-order compact finite difference scheme for one-dimensional Burgers' equation
    • Wenyuan Liao An implicit fourth-order compact finite difference scheme for one-dimensional Burgers' equation Appl. Math. Comput. 206 2008 755 764
    • (2008) Appl. Math. Comput. , vol.206 , pp. 755-764
    • Liao, W.1
  • 29
    • 78649492432 scopus 로고    scopus 로고
    • An improved numerical solution of Burgers' equation by cubic B-spline Quasi-interpolation
    • Ziwu Jiang, and Renhong Wang An improved numerical solution of Burgers' equation by cubic B-spline Quasi-interpolation J. Inform. Comput. Sci. 7 5 2010 1013 1021
    • (2010) J. Inform. Comput. Sci. , vol.7 , Issue.5 , pp. 1013-1021
    • Jiang, Z.1    Wang, R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.