메뉴 건너뛰기




Volumn 27, Issue 1, 2011, Pages 69-77

Numerical solutions of linear and nonlinear diffusion equations by a differential quadrature method (DQM)

Author keywords

Differential quadrature (DQ); Diffusion equation; Nonlinear PDE; Runge Kutta method; Strong stability preserving

Indexed keywords

ALTERNATIVE METHODS; APPROXIMATE SOLUTION; DIFFERENTIAL QUADRATURE; DIFFERENTIAL QUADRATURE METHODS; DIFFUSION EQUATION; EXACT SOLUTION; NON LINEAR PDE; NONLINEAR DIFFUSION EQUATIONS; NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS; NUMERICAL ERRORS; NUMERICAL SOLUTION; PHYSICAL MODEL; RUNGE-KUTTA; STORAGE SPACES; STRONG STABILITY PRESERVING;

EID: 78650698074     PISSN: 20407939     EISSN: 20407947     Source Type: Journal    
DOI: 10.1002/cnm.1292     Document Type: Article
Times cited : (23)

References (24)
  • 1
    • 0001301093 scopus 로고    scopus 로고
    • The non-classical solution of the inhomogeneous non-linear diffusion equation
    • Saied EA. The non-classical solution of the inhomogeneous non-linear diffusion equation. Applied Mathematics and Computation 1999; 98(2-3):103-108.
    • (1999) Applied Mathematics and Computation , vol.98 , Issue.2-3 , pp. 103-108
    • Saied, E.A.1
  • 2
    • 21344491154 scopus 로고
    • New classes of similarity solutions of the inhomogeneous nonlinear diffusion equations
    • Saied EA, Hussein MM. New classes of similarity solutions of the inhomogeneous nonlinear diffusion equations. Journal of Physics-London-A Mathematical and General 1994; 27:4867-4874.
    • (1994) Journal of Physics-London-A Mathematical and General , vol.27 , pp. 4867-4874
    • Saied, E.A.1    Hussein, M.M.2
  • 3
    • 0003737626 scopus 로고
    • Similarity Solutions of Nonlinear Partial Differential Equations
    • Pitman: New York.
    • Dresner L. Similarity Solutions of Nonlinear Partial Differential Equations. Pitman: New York, 1983.
    • (1983)
    • Dresner, L.1
  • 4
    • 6544263763 scopus 로고    scopus 로고
    • Exact solutions to nonlinear diffusion equations obtained by a generalized conditional symmetry method
    • Changzheng Q. Exact solutions to nonlinear diffusion equations obtained by a generalized conditional symmetry method. IMA Journal of Applied Mathematics 1999; 62:283-302.
    • (1999) IMA Journal of Applied Mathematics , vol.62 , pp. 283-302
    • Changzheng, Q.1
  • 5
    • 0003991257 scopus 로고
    • Symmetries and Differential Equations
    • Springer: New York.
    • Bluman GW, Kumei S. Symmetries and Differential Equations. Springer: New York, 1989.
    • (1989)
    • Bluman, G.W.1    Kumei, S.2
  • 7
    • 0003444747 scopus 로고
    • Nonlinear Partial Differential Equations
    • Academic Press: New York.
    • Ames WF. Nonlinear Partial Differential Equations. Academic Press: New York, 1972.
    • (1972)
    • Ames, W.F.1
  • 8
    • 0003429751 scopus 로고
    • Applications of Nonlinear Analysis in the Physical Sciences
    • Amann H, Bazley N, Kirchgassner K (eds). Pitman: London.
    • Peletier LA. The porous media equation. In Applications of Nonlinear Analysis in the Physical Sciences, Amann H, Bazley N, Kirchgassner K (eds). Pitman: London, 1981; 229.
    • (1981) The porous media equation , pp. 229
    • Peletier, L.A.1
  • 9
    • 0035840358 scopus 로고    scopus 로고
    • Exact solutions to nonlinear diffusion equations obtained by the decomposition method
    • Wazwaz AM. Exact solutions to nonlinear diffusion equations obtained by the decomposition method. Applied Mathematics and Computation 2001; 123(1):109-122.
    • (2001) Applied Mathematics and Computation , vol.123 , Issue.1 , pp. 109-122
    • Wazwaz, A.M.1
  • 11
    • 0032243643 scopus 로고    scopus 로고
    • Linear determining equations for differential constraints
    • Kaptsov OV. Linear determining equations for differential constraints. Sbornik: Mathematics 1998; 189(12):1839-1854.
    • (1998) Sbornik: Mathematics , vol.189 , Issue.12 , pp. 1839-1854
    • Kaptsov, O.V.1
  • 12
    • 0043023557 scopus 로고    scopus 로고
    • Several new exact solutions for a fast diffusion equation by the differential constraints of the linear determining equations
    • Wazwaz AM. Several new exact solutions for a fast diffusion equation by the differential constraints of the linear determining equations. Applied Mathematics and Computation 2003; 145(2-3):525-540.
    • (2003) Applied Mathematics and Computation , vol.145 , Issue.2-3 , pp. 525-540
    • Wazwaz, A.M.1
  • 13
    • 34748875886 scopus 로고    scopus 로고
    • The variational iteration method: a powerful scheme for handling linear and nonlinear diffusion equations
    • Wazwaz AM. The variational iteration method: a powerful scheme for handling linear and nonlinear diffusion equations. Computers and Mathematics with Applications 2007; 54(7-8):933-939.
    • (2007) Computers and Mathematics with Applications , vol.54 , Issue.7-8 , pp. 933-939
    • Wazwaz, A.M.1
  • 14
    • 0002800312 scopus 로고
    • Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations
    • Bellman R, Kashef BG, Casti J. Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations. Journal of Computational Physics 1972; 10(1):40-52.
    • (1972) Journal of Computational Physics , vol.10 , Issue.1 , pp. 40-52
    • Bellman, R.1    Kashef, B.G.2    Casti, J.3
  • 15
    • 0029724421 scopus 로고    scopus 로고
    • Differential quadrature method in computational mechanics: a review
    • Bert CW, Malik M. Differential quadrature method in computational mechanics: a review. Applied Mechanics Reviews 1996; 49(1):1-27.
    • (1996) Applied Mechanics Reviews , vol.49 , Issue.1 , pp. 1-27
    • Bert, C.W.1    Malik, M.2
  • 16
    • 78650701717 scopus 로고
    • Generalized differential-integral quadrature and application to the simulation of incompressible viscous flows including parallel computation. Ph.D. Thesis, University of Glasgow, U.K..
    • Shu C. Generalized differential-integral quadrature and application to the simulation of incompressible viscous flows including parallel computation. Ph.D. Thesis, University of Glasgow, U.K., 1991.
    • (1991)
    • Shu, C.1
  • 17
    • 0026939625 scopus 로고
    • Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations
    • Shu C, Richards BE. Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations. International Journal for Numerical Methods in Fluids 1992; 15(7):791-798.
    • (1992) International Journal for Numerical Methods in Fluids , vol.15 , Issue.7 , pp. 791-798
    • Shu, C.1    Richards, B.E.2
  • 18
    • 33646081035 scopus 로고    scopus 로고
    • Approximations of Sturm-Liouville eigenvalues using differential quadrature (DQ) method
    • Yücel U. Approximations of Sturm-Liouville eigenvalues using differential quadrature (DQ) method. Journal of Computational and Applied Mathematics 2006; 192(2):310-319.
    • (2006) Journal of Computational and Applied Mathematics , vol.192 , Issue.2 , pp. 310-319
    • Yücel, U.1
  • 19
    • 0036815601 scopus 로고    scopus 로고
    • A localized differential quadrature (LDQ) method and its applications to the 2D wave equation
    • Zong Z, Lam KY. A localized differential quadrature (LDQ) method and its applications to the 2D wave equation. Computational Mechanics 2002; 29:382-391.
    • (2002) Computational Mechanics , vol.29 , pp. 382-391
    • Zong, Z.1    Lam, K.Y.2
  • 20
    • 41949083257 scopus 로고    scopus 로고
    • Differential quadrature method for singularly perturbed two-point boundary value problems
    • Sari M. Differential quadrature method for singularly perturbed two-point boundary value problems. Journal of Applied Sciences 2008; 8(6):1091-1096.
    • (2008) Journal of Applied Sciences , vol.8 , Issue.6 , pp. 1091-1096
    • Sari, M.1
  • 21
    • 61449123934 scopus 로고    scopus 로고
    • Differential quadrature method (DQM) for a class of singular two-point boundary value problems
    • Yücel U, Sari M. Differential quadrature method (DQM) for a class of singular two-point boundary value problems. International Journal of Computer Mathematics 2009; 86(3):465-475.
    • (2009) International Journal of Computer Mathematics , vol.86 , Issue.3 , pp. 465-475
    • Yücel, U.1    Sari, M.2
  • 22
    • 65349171462 scopus 로고    scopus 로고
    • Numerical solutions of the generalized Burgers-Huxley equation by a differential quadrature method (DQM)
    • Article ID 370765.
    • Sari M, Gürarslan G. Numerical solutions of the generalized Burgers-Huxley equation by a differential quadrature method (DQM). Mathematical Problems in Engineering 2009; Article ID 370765.
    • (2009) Mathematical Problems in Engineering
    • Sari, M.1    Gürarslan, G.2
  • 23
    • 0003430690 scopus 로고    scopus 로고
    • Differential Quadrature and its Application in Engineering
    • Springer: London.
    • Shu C. Differential Quadrature and its Application in Engineering. Springer: London, 2000.
    • (2000)
    • Shu, C.1
  • 24
    • 0035273564 scopus 로고    scopus 로고
    • Strong stability-preserving high-order time discretization methods
    • Gottlieb S, Shu C-W, Tadmor E. Strong stability-preserving high-order time discretization methods. SIAM Review 2001; 43(1):89-112.
    • (2001) SIAM Review , vol.43 , Issue.1 , pp. 89-112
    • Gottlieb, S.1    Shu, C.2    Tadmor, E.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.