Literature cited
M. N. Yakovlev, “Nonnegative solutions of second-order quasilinear equations,” Trudy Matem. Inst. Akad. Nauk SSSR,96, 105–110 (1968).
M. E. Rose, “On the integration of nonlinear parabolic equations by implicit difference methods methods,” Quart. Appl. Math.,14, 237–248 (1956/57).
A. A. Samarskii, “Homogeneous difference schemes for nonlinear parabolic equations,” Zh. Vychisl. Matem. i Matem. Fiz.,2, No. 1, 25–56 (1962).
R. Krawezyk, “Über Differenzenverfahren bei parabolische Differentialgleichungen,” Arch. Rat. Mech. Anal.,13, 81–121 (1963).
M. Lees, “Approximate solution of parabolic equations,” J. Soc. Indust. Appl. Math.,7, 167–183 (1959).
E. Schechter, “Stability and convergence criteria for nonlinear parabolic difference equations,” Mathematica,10(33), No. 1, 127–150 (1968).
E. N. Gorovaya and V. Ya. Rivkind, “Difference method for solving quasilinear elliptic and parabolic equations with discontinuous coefficients,” Metody Vychislenii,6, 22–41 (1970).
R. Gorenflo, “Differenzenschemata monotoner Art für schwach gekoppelte Systeme parabolischer Differentialgleichungen mit gemischten Randbedingungen,” Computing,8, No. 3–4, 343–362 (1971).
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 35, pp. 160–166, 1973.
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Yakovlev, M.N. Implicit difference method for solving the first boundary-value problem for a second-order nonlinear parabolic equation. J Math Sci 7, 123–127 (1977). https://doi.org/10.1007/BF01846082
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DOI: https://doi.org/10.1007/BF01846082