Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/111607
Title: On Solving Non-homogeneous Partial Differential Equations with Right-hand Side Defined on the Grid
Other Titles: К решению неоднородных уравнений в частных производных с правой частью, заданной на сетке
Authors: Rubina, L. I.
Ul’yanov, O. N.
Issue Date: 2021
Publisher: Udmurt State University
Udmurt State University
Citation: Rubina L. I. On Solving Non-homogeneous Partial Differential Equations with Right-hand Side Defined on the Grid [К решению неоднородных уравнений в частных производных с правой частью, заданной на сетке] / L. I. Rubina, O. N. Ul’yanov // Vestnik Udmurtskogo Universiteta: Matematika, Mekhanika, Komp'yuternye Nauki. — 2021. — Vol. 31. — Iss. 3. — P. 443-457.
Abstract: An algorithm is proposed for obtaining solutions of partial differential equations with right-hand side defined on the grid {xµ1 , xµ2 , . . ., xµn}, (µ = 1, 2, . . ., N): fµ = f (xµ1 , xµ2 , . . ., xµn). Here n is the number of independent variables in the original partial differential equation, N is the number of rows in the grid for the right-hand side, f = f (x1, x2, . . ., xn) is the right-hand of the original equation. The algorithm implements a reduction of the original equation to a system of ordinary differential equations (ODE system) with initial conditions at each grid point and includes the following sequence of actions. We seek a solution to the original equation, depending on one independent variable. The original equation is associated with a certain system of relations containing arbitrary functions and including the partial differential equation of the first order. For an equation of the first order, an extended system of equations of characteristics is written. Adding to it the remaining relations containing arbitrary functions, and demanding that these relations be the first integrals of the extended system of equations of characteristics, we arrive at the desired ODE system, completing the reduction. The proposed algorithm allows at each grid point to find a solution of the original partial differential equation that satisfies the given initial and boundary conditions. The algorithm is used to obtain solutions of the Poisson equation and the equation of unsteady axisymmetric filtering at the points of the grid on which the right-hand sides of the corresponding equations are given. © 2021 Udmurt State University. All rights reserved.
Keywords: EXTENDED SYSTEM OF CHARACTERISTICS EQUATIONS
PARTIAL DIFFERENTIAL EQUATIONS
REDUCTION OF PDES TO ODE SYSTEMS
SOLUTION OF INITIAL AND BOUNDARY VALUE PROBLEMS
URI: http://hdl.handle.net/10995/111607
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85117108368
PURE ID: 23818926
ISSN: 1994-9197
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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