Spectral methods in time for a class of parabolic partial differential equations

Journal Article · Tue Sep 01 00:00:00 EDT 1992 · Journal of Computational Physics; (United States)

DOI:https://doi.org/10.1016/S0021-9991(05)80008-7· OSTI ID:7049037

Ierley, G ^[1]; Spencer, B ^[2]; Worthing, R ^[3]

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1. Michigan Technological Univ., Houghton, MI (United States)
2. Northwestern Univ., Evanston, IL (United States)
3. MIT, Cambridge, MA (United States)

In this paper, we introduce a fully spectral solution for the partial differential equation u[sub t] + uu[sub x] + vu[sub xx] + [mu]u[sub xxx] + [lambda]u[sub xxxx] = O. For periodic boundary conditions in space, the use of a Fourier expansion in x admits of a particularly efficient algorithm with respect to expansion of the time dependence in a Chebyshev series. Boundary conditions other than periodic may still be treated with reasonable, though lesser, efficiency. for all cases, very high accuracy is attainable at moderate computational cost relative to the expense of variable order finite difference methods in time. 14 refs., 9 figs.

• OSTI ID: 7049037
• Journal Information: Journal of Computational Physics; (United States), Journal Name: Journal of Computational Physics; (United States) Vol. 102:1; ISSN 0021-9991; ISSN JCTPAH
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
CALCULATION METHODS
COMPARATIVE EVALUATIONS
DIFFERENTIAL EQUATIONS
EFFICIENCY
EQUATIONS
EVALUATION
ITERATIVE METHODS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS