메뉴 건너뛰기




Volumn 31, Issue 6, 1996, Pages 97-115

A comparison of some adaptive space mesh solvers for the numerical solution of parabolic partial differential equations

Author keywords

Adaptive solvers; Method of lines; Moving grids; Partial differential equations; Time dependent problems

Indexed keywords


EID: 0040159668     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/0898-1221(96)00009-0     Document Type: Article
Times cited : (3)

References (22)
  • 2
    • 0002753571 scopus 로고
    • A description of DASSL: A differential/algebraic system solver
    • (Edited by R.S. Stepleman), North Holland
    • L.R. Petzold, A description of DASSL: A differential/algebraic system solver, In Scientific Computing, (Edited by R.S. Stepleman), pp. 65-68, North Holland, (1983).
    • (1983) Scientific Computing , pp. 65-68
    • Petzold, L.R.1
  • 4
    • 0002054204 scopus 로고
    • A method for the spatial discretization of parabolic equations in one space variable
    • R.D. Skeel and M. Berzins, A method for the spatial discretization of parabolic equations in one space variable, SIAM J. Sci. Stat. Comp. 11, 1-32 (1990).
    • (1990) SIAM J. Sci. Stat. Comp. , vol.11 , pp. 1-32
    • Skeel, R.D.1    Berzins, M.2
  • 6
    • 0022046824 scopus 로고
    • A moving mesh finite element method with local refinement for parabolic partial differential equations
    • S. Adjerid and J.E. Flaherty, A moving mesh finite element method with local refinement for parabolic partial differential equations, Comp. Meths. Appl. Mech. Engr. 56, 3-26 (1986).
    • (1986) Comp. Meths. Appl. Mech. Engr. , vol.56 , pp. 3-26
    • Adjerid, S.1    Flaherty, J.E.2
  • 9
    • 0002445594 scopus 로고
    • LSODE and LSODI: Two new initial-value ordinary differential equation solvers
    • A.C. Hindmarsh, LSODE and LSODI: Two new initial-value ordinary differential equation solvers, ACM SIGNUM Newsletter 15, 10-11 (1980).
    • (1980) ACM SIGNUM Newsletter , vol.15 , pp. 10-11
    • Hindmarsh, A.C.1
  • 10
    • 0001811061 scopus 로고
    • ODEPACK: A systematized collection of ODE solvers
    • (Edited by R.S. Stepleman), IMACS, North-Holland, Amsterdam
    • A.C. Hindmarsh, ODEPACK: A systematized collection of ODE solvers, In Scientific Computing, (Edited by R.S. Stepleman), pp. 55-64, IMACS, North-Holland, Amsterdam, (1983).
    • (1983) Scientific Computing , pp. 55-64
    • Hindmarsh, A.C.1
  • 11
    • 84976857655 scopus 로고
    • Software for nonlinear partial differential equations
    • R.F. Sincovec and N.K. Madsen, Software for nonlinear partial differential equations, ACM Trans. Math. Software 1, 232-260 (1975).
    • (1975) ACM Trans. Math. Software , vol.1 , pp. 232-260
    • Sincovec, R.F.1    Madsen, N.K.2
  • 12
    • 0019610768 scopus 로고
    • A set of library routines for solving parabolic equations in one space dimension
    • P.M. Dew and J.E. Walsh, A set of library routines for solving parabolic equations in one space dimension, ACM Trans. Math. Software 7, 295-314 (1981).
    • (1981) ACM Trans. Math. Software , vol.7 , pp. 295-314
    • Dew, P.M.1    Walsh, J.E.2
  • 13
    • 0018517232 scopus 로고
    • Algorithm 540: PDECOL general collocation software for partial differential equations
    • N.K. Madsen and R.F. Sincovec, Algorithm 540: PDECOL general collocation software for partial differential equations, ACM Trans. Math. Software 5, 326-351 (1979).
    • (1979) ACM Trans. Math. Software , vol.5 , pp. 326-351
    • Madsen, N.K.1    Sincovec, R.F.2
  • 15
    • 0039686443 scopus 로고
    • Adaptive overlapping grid methods for parabolic systems
    • (Edited by J. Paslow, M.S. Shepherd and J.D. Vasilakis), SIAM, Philadelphia
    • J.E. Flaherty, P.K. Moore and C. Ozturan, Adaptive overlapping grid methods for parabolic systems, In Adaptive Methods for Partial Differential Equations, (Edited by J. Paslow, M.S. Shepherd and J.D. Vasilakis), pp. 176-193, SIAM, Philadelphia, (1989).
    • (1989) Adaptive Methods for Partial Differential Equations , pp. 176-193
    • Flaherty, J.E.1    Moore, P.K.2    Ozturan, C.3
  • 16
    • 0022768316 scopus 로고
    • A moving finite element method with error estimation and refinement for one-dimensional time dependent partial differential equations
    • S. Adjerid and J.E. Flaherty, A moving finite element method with error estimation and refinement for one-dimensional time dependent partial differential equations, SIAM J. Numer. Anal., 23, 778-796 (1986).
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 778-796
    • Adjerid, S.1    Flaherty, J.E.2
  • 17
    • 0040872544 scopus 로고
    • Note on finite difference approximations to Burgers' equation
    • H. Aref and P.K. Darpia, Note on finite difference approximations to Burgers' equation, SIAM J. Sci. Stat. Comp. 5, 856-863 (1984).
    • (1984) SIAM J. Sci. Stat. Comp. , vol.5 , pp. 856-863
    • Aref, H.1    Darpia, P.K.2
  • 18
    • 0000984027 scopus 로고
    • On simple moving grid methods for one-dimensional evolutionary partial differential equations
    • J.G. Blom, J.M. Sanz-Serna and J.G. Verwer, On simple moving grid methods for one-dimensional evolutionary partial differential equations, J. Comput. Phys. 74, 191-213 (1988).
    • (1988) J. Comput. Phys. , vol.74 , pp. 191-213
    • Blom, J.G.1    Sanz-Serna, J.M.2    Verwer, J.G.3
  • 19
    • 0039094199 scopus 로고
    • An adaptive finite element method for initial-boundary value problems for parabolic differential equations
    • S.F. Davis and J.E. Flaherty, An adaptive finite element method for initial-boundary value problems for parabolic differential equations, SIAM J. Sci. Stat. Comp. 3, 6-27 (1982).
    • (1982) SIAM J. Sci. Stat. Comp. , vol.3 , pp. 6-27
    • Davis, S.F.1    Flaherty, J.E.2
  • 20
    • 0023393821 scopus 로고
    • Observations on an adaptive moving grid method for one-dimensional systems of partial differential equations
    • L.R. Petzold, Observations on an adaptive moving grid method for one-dimensional systems of partial differential equations, Appl. Numerical Maths. 3, 347-360 (1987).
    • (1987) Appl. Numerical Maths. , vol.3 , pp. 347-360
    • Petzold, L.R.1
  • 21
    • 0001121137 scopus 로고
    • Simple adaptive grids for 1-D initial value problems
    • E.A. Dorfi and L.O. Drury, Simple adaptive grids for 1-D initial value problems, J. Comput. Phys. 69, 175-195 (1987).
    • (1987) J. Comput. Phys. , vol.69 , pp. 175-195
    • Dorfi, E.A.1    Drury, L.O.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.