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Long-range numerical solution of mildly non-linear parabolic equations

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Summary

We analyze the convergence of a “boundary-value” procedure for numerically solving the mildly non-linear parabolic equation,

$$u_t = [a (x, t) u_x ]_x + b (x, t) u_x - f(x, t, u)$$

, wherea(x, t) ≧a 0>0, andf u ≧0, and the solutionu reaches a steady state ast → ∞. Such a procedure yields an error estimate, which is uniform int. We also discuss an iterative method of solving the difference equations.

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Authors and Affiliations

  1. Dep. of Mathematics and Statistics, Univ. of New Mexico, 87106, Albuquerque, New Mexico

    Alfred Carasso

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  1. Alfred Carasso
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Partly supported by ONR contract No. N 0014-67-A-0128-004.

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Carasso, A. Long-range numerical solution of mildly non-linear parabolic equations. Numer. Math. 16, 304–321 (1971). https://doi.org/10.1007/BF02165002

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  • DOI: https://doi.org/10.1007/BF02165002

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