Difference potentials analogous to Cauchy integrals

V. S. Ryaben'kii

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 67 (2012) no. 3, pp. 541-567

Résumé

This work presents the state of the art in the theory of potentials for the solutions of systems of linear difference equations, which was proposed by the author in 1969. The role played by difference potentials in the solution of linear difference schemes of general form is for the first time compared in detail to the role played by Cauchy-type integrals in the theory of analytic functions. New vistas are exposed, which are opened up by the theory of difference potentials and arise through combining the universality and algorithmicity of difference schemes with certain properties of Cauchy-type integrals. A brief bibliographical review covers some of the fundamental applications of the theory which have already been implemented. Bibliography: 61 titles.

Détail

Keywords: difference potentials, Cauchy integrals, numerical solution of boundary value problems, artificial boundary conditions, mathematical theory of noise control.

Bibliographie

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