Abstract
In this paper with simple examples there is examined one of the improvement methods of approximate solution, which is derived with integral equalities for elliptic differential problems. The improvement method is to use some approximate systems having low order of accuracy and depending on the mesh size as the parameter. A linear combination of solutions of these problems is made, which has a given order of accuracy limited by only a degree of smoothness and the data of the differential problem.
An idea of this method is due to L.F.Richardson, but E.A.Volkov and some other mathematicians obtained a constructive proof for some problems in the 1950's.
We research the realization of this method for an ordinary differential equation (in detail, as as illustration), an elliptic differential equation in a rectangle and in the domain with a smooth boundary, and an evolutional equation with a bounded operator.
Chapter PDF
Similar content being viewed by others
Literature
G.I.Marchuk. Methods of computing mathematics. Novosibirsk, "Nauka", 1973.
R.Bellman. Introduction in matrix theory. New York, Toronto, London, 1960.
S.L.Sobolev. Some applications of functional analysis in mathematical physics. Printed by Siberian Brunch of AS of the USSR, Novosibirsk, 1962.
E.A.Volkov. Solving Dirichlet's problem by: method of improvement by higher order differences "Differential equations", v. 1, No 7, 8, 1965.
O.A. Ladizenskaja, N.N. Uraltzeva. Linear and quasi-linear equations of elliptic type. Moscow, "Nauka", 1964.
J.L.Lions. Quelques méthodes de résolution des problèmes aux limites non linéaires. Paris, 1969.
A.A. Samarski. Introduction in theory of difference schemes. Moscow, "Nauka", 1971.
H.Cartan. Calcul différentiel. Formes différentielles. Paris, 1967.
Editor information
Rights and permissions
Copyright information
© 1974 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Marchuk, G.I., Shaydourov, V.V. (1974). Increase of accuracy of projective-difference schemes. In: Glowinski, R., Lions, J.L. (eds) Computing Methods in Applied Sciences and Engineering Part 2. Lecture Notes in Computer Science, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-06769-8_11
Download citation
DOI: https://doi.org/10.1007/3-540-06769-8_11
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-06769-6
Online ISBN: 978-3-540-38380-2
eBook Packages: Springer Book Archive