Abstract
We consider the first mixed problem for nonlinear parabolic equation. Assuming that the exact solution of the problem is u(t,x,y) ∈ C4,−0(Q), Q={(x,y)∈Ω, 0⩽t⩽T} we construct a scheme of the method of straight lines of accuracy 0(h2) for the cases when ώ is a rectangle or a trapezoid.
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Literature cited
M. N. Yakovlev, “Estimating the approximate solution of the Cauchy problem,” in: Numerical Methods and Functional Analysis, J. Soy. Math.,2, No. 4 (1974).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 159, pp. 132–142, 1987.
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Kubanskaya, A.P. Method of straight lines in application to some two-dimensional nonlinear parabolic equations. J Math Sci 47, 2917–2926 (1989). https://doi.org/10.1007/BF01305223
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DOI: https://doi.org/10.1007/BF01305223