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Approximation of the solution of the mixed problem for a parabolic equation. (Russian) Zbl 0637.35041
Investigations on the theory of approximation of functions, Work Collect., Ufa 1984, 50-58 (1984).
[For the entire collection see Zbl 0622.00009.]
Recurrent formulas are obtained for the approximation of the solution of mixed problems for a parabolic equation by linear combinations of eigenfunctions of the Laplace operator. These formulas can be considered as a generalization of results of a previous work by the author [Sov. Math., Dokl. 21, 117-121 (1980); translation from Dokl. Akad. Nauk SSSR 250, 535-539 (1980; Zbl 0448.35035)] to the case where coefficients of the elliptic part of the equation depend on time and boundary conditions are non-homogeneous.
MSC:
35K10 Second-order parabolic equations
35A35 Theoretical approximation in context of PDEs
35P10 Completeness of eigenfunctions and eigenfunction expansions in context of PDEs
35C05 Solutions to PDEs in closed form