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Kurpel’, N. S.; Maiboroda, I. N.

A method of constructing two-sided approximations to solutions of operator equations. (English) Zbl 0355.65047

Ukr. Math. J. 28(1976), 467-474 (1977).
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MSC:

65J05 General theory of numerical analysis in abstract spaces
49M20 Numerical methods of relaxation type
47J05 Equations involving nonlinear operators (general)
46A40 Ordered topological linear spaces, vector lattices
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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References:

[1] S. A. Chaplygin, A New Approximation Method for Integrating Differential Equations [in Russian], Gostekhizdat, Moscow-Leningrad (1950).
[2] N. N. Luzin, ?On the Chaplygin method of approximate integration,? Trudy TsAGI,141, 3-30 (1932).
[3] B. A. Bertgeim, ?On the speed of convergence of the approximations in Chaplygin’s method and in modifications of this method,? in: Nauchn. Trudy Permskogo Gornogo In-ta, No. 1 (1956), pp. 136-141.
[4] N. S. Kurpel’, ?Modifications of the Chaplygin method of approximate integration of differential equations,? Dopov. Akad. Nauk URSR, Ser. A, No. 4, 303-306 (1969).
[5] N. S. Kurpel’, ?Some generalizations and modifications of the Chaplygin method,? in: Approximate and Qualitative Methods in the Theory of Differential and Integral Equations, Izd. Instituta Matematiki Akad. Nauk UkrSSR, Kiev (1971), pp. 51-72.
[6] A. M. Il’-in, A. S. Kalashnikov, and O. A. Oleinik, ?Second-order linear equations of parabolic type,? Ukrainsk. Matem. Zh.,17, No. 3(105), 4-146 (1962).
[7] P. K. Zeragiya, ?Solution of a fundamental boundary-value problem for a class of nonlinear parabolic differential equations by the Chaplygin method,? in: Trudy Tbilisskogo Un-ta, A6-7(149-150) (1973), pp. 17-27.
[8] É. Ya. Sentebova and M. V. Tolstopyatova, ?The Newton-Kantorovich method for the heat-production equation with a retarded argument,? in: Trudy Moskovskogo In-ta Khimocheskogo Mashinostroeniya, Vol. 39 (1972), pp. 41-43.
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