Abstract
We construct an approximate solution for an initial boundary-value problem of the formu t (x, t) + a (x, t) ux (x, t)=b (x, t, u), u (x, 0)=u0 (x),u (0,t)=u1 (t) by the method of characteristics. It is proved that the approximate solution converges to the exact one with rate of convergence of second order.
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V. L. Rozhdestvenskii and N. N. Yanenko, Systems of Quasilinear Equations [in Russian], Nauka, Moscow (1968).
N. P. Korneichuk, Splines in Approximations Theory [in Russian], Nauka, Moscow (1984).
Khoang Van Lai, “Application of splines in approximate determination of the classical solution of the Cauchy problem for a quasilinear equation of first order,” Ukr. Mat. Zh.,39, No. 4, 501–506 (1987).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 8, pp. 1128–1138, August, 1990.
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Van Lai, K. Convergence of the method of characteristics in approximate solution of a semilinear partial differential equation of first order. Ukr Math J 42, 1006–1015 (1990). https://doi.org/10.1007/BF01099235
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DOI: https://doi.org/10.1007/BF01099235