Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
BRANDT, A., Multi-level adaptive techniques (MLAT) for singular perturbation problems. In Numerical Analysis of singular perturbation problems, P.W. Hemker and J.J.H. Miller eds., Academic Press, 1979.
FRANK, W., Solution of linear systems by Richardson's method, J. Assoc. Comput. Mach. 7, 274–286 (1960).
FORSYTHE, G.E. & WASOW, W.R., Finite difference methods for partial differential equations, John Wiley, New York (1960).
GENTZSCH, W. & SCHLŰTER, A., “Űber ein Einschrittverfahren mit zyklischer Schrittweitenänderung zur Lősung parabolischer Differentialgleichungen ZAMM 58, T415–T416 (1978).
HEMKER, P.W., Introduction to multigrid methods, Nieuw Arch. voor Wiskunde 29, 71–101 (1981).
-, On the structure of an adaptive multi-level algorithm, BIT 20, 289–301 (1980).
HOUWEN, P.J. VAN DER, Construction of integration formulas for initial value problems, North-Holland (1977).
HOUWEN, P.J. VAN DER & SOMMEIJER, B.P., On the internal stability of explicit, m-stage Runge-Kutta methods for large m-values ZAMM 60, 479–485 (1980).
HOUWEN, P.J. VAN DER & SOMMEIJER, B.P., Analysis of Richardson iteration in multigrid methods for nonlinear parabolic differential equations, Report NW105/81, Math. Centrum, Amsterdam 1981 (prepublication).
JELTSCH, R. & NEVANLINNA, O., Stability of explicit time discretizations for solving initial value problems, Report no. 30, University of Oulu 1979 (prepublication).
LOMAX, H., On the construction of highly stable, explicit, numerical methods for integrating coupled ordinary differential equations with parasitic eignevalues, NASA Technical Note NASATN D/4547 (1968).
MANTEUFFEL, T.A., The Techebyshev iteration for non-symmetric linear systems, Num. Math. 28, 307–327 (1977).
METZGER, CL. Méthodes de Runge-Kutta de rang supérieur à l'ordre. These (troisieme cycle), Université de Grenoble (1967).
RIHA, W., Optimal stability polynomials, Computing 9, 37–43 (1972).
SAUL'YEV, V.K., Integration of equations of parabolic type by the methods of nets, Pergamon Press, New York (1964).
SOMMEIJER, B.P. & VERWER, J.G., A performance evaluation of a class of Runge-Kutta-Chebyshev methods for solving semi-discrete parabolic differential equations, Report NW 91/80, Math. Centrum, Amsterdam (1980).
STETTER, H.J., Analysis of discretization methods for ordinary differential equations, Springer-Verlag, Berlin (1973).
-, The defect correction principle and discretization methods, Num. Math. 29, 425–443 (1978).
YUAN'CHZHAO-DIN, Some difference schemes for the solution of the first boundary value problem for linear differential equations with partial derivatives, Thesis, Moscow State University (1958).
Editor information
Rights and permissions
Copyright information
© 1982 Springer-Verlag
About this paper
Cite this paper
van der Houwen, P.J. (1982). On the time integration of parabolic differential equations. In: Watson, G.A. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 912. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0093155
Download citation
DOI: https://doi.org/10.1007/BFb0093155
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-11199-3
Online ISBN: 978-3-540-39009-1
eBook Packages: Springer Book Archive