An unconditionally stable and O(τ2+ h4) order L∞convergent difference scheme for linear parabolic equations with variable coefficients
In: Numerical Methods for Partial Differential Equations, Jg. 17 (2001-11-01), Heft 6, S. 619-631
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Zugriff:
M. K. Jain, R. K. Jain, and R. K. Mohanty presented a finite difference scheme of O(τ2+ τh2+ h4) for solving the one‐dimensional quasilinear parabolic partial differential equation, uxx= f(x, t, u, ut, ux), with Dirichlet boundary conditions. The method, when applied to a linear constant coefficient case, was shown to be unconditionally stable by the Von Neumann method. In this article, we prove that the method, when applied to a linear variable coefficient case, is unconditionally stable and convergent with the convergence order O(τ2+ h4) in the L∞‐norm. In addition, we obtain an asymptotic expansion of the difference solution, with which we obtain an O(τ4+ τ2h4+ h6) order accuracy approximation after extrapolation. And last, we point out that the analysis method in this article is efficacious for complex equations. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17:619–631, 2001
Titel: |
An unconditionally stable and O(τ2+ h4) order L∞convergent difference scheme for linear parabolic equations with variable coefficients
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Autor/in / Beteiligte Person: | Sun, Zhi‐Zhong |
Link: | |
Zeitschrift: | Numerical Methods for Partial Differential Equations, Jg. 17 (2001-11-01), Heft 6, S. 619-631 |
Veröffentlichung: | 2001 |
Medientyp: | serialPeriodical |
ISSN: | 0749-159X (print) ; 1098-2426 (print) |
DOI: | 10.1002/num.1030 |
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