Abstract
We investigate the applicability of the method of lines to delayed equations. We consider a boundary-value problem for a quasilinear parametric equation with delay in the right-hand side. The scheme of the method of lines is shown to be second-order convergent when the delay is constant and nonnegative and the function f is Lipschitzian in the third argument in the class W2 2(QT).
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Translated from Vychislitel'naya i Prikladnaya Matematika, No. 62, pp. 20–26, 1987.
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Kopystyra, N.P., Sakhtaganova, A.T. Convergence of the method of lines for one quasilinear parabolic equation with delay. J Math Sci 63, 522–527 (1993). https://doi.org/10.1007/BF01142523
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DOI: https://doi.org/10.1007/BF01142523