Explicit Hermitian Methods for the Numerical Solution of Parabolic Partial Differential Equations
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Explicit hermitian methods, which have smaller truncation errors and better stability properties than presently available explicit methods, are derived for the one-dimensional nonhomogeneous parabolic differential equation. As these hermitian methods are not defined for all internal points of the difference grid used, smoothing methods which enable their practical application are formulated. Numerical results for a linear and a nonlinear example are given.
KeywordsBurger Equation Discretization Error Parabolic Partial Differential Equation Difference Grid Parabolic Differential Equation
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- Benton, E.R. and Platzmann, G.W.: A table of solutions of the one-dimensional Burgers equation. Quarterly of Applied Maths. 30 (1972), 195–212.Google Scholar
- Collatz, L.: Hermitian methods for initial value problems in partial differential equations. Topics in Numerical Analysis, Proceedings of the Royal Irish Academy Conference on Numerical Analysis, 1972. Edited by J.J.H. Miller. London, Academic 1973.Google Scholar
- Richtmyer, R.D. and Morton, K.W.: Difference Methods for Initial Value Problems. New York, Interscience 1967.Google Scholar