Goursat boundary value problem
type: Item
instance of: scholarly article
zbMATH Open document ID: 0974.65097
author: V. L. Rego
publication date: 2001-08-08T00:00:00Z
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 35G30
zbMATH DE Number: 1631418
zbMATH Keywords: Goursat boundary value problem
zbMATH Keywords: bilateral method
zbMATH Keywords: system of partial differential equations
zbMATH Keywords: consistency
MaRDI profile type: Publication
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title: Goursat boundary value problem
published in: Naukovyĭ Visnyk Uzhgorods'kogo Universytetu. Seriya Matematyka
review text: The author proposes an algorithm of bilateral method for the approximate integration of the system of partial differential equations NEWLINE\[NEWLINED^{(1,1)} u_{i}(x,y)=f_{i}(x,y,u,D^{(1,0)}u, D^{(0,1)}u), \quad i=1,2;NEWLINE\]NEWLINE NEWLINE\[NEWLINEu=(u_1(x,y),u_2(x,y)), \quad D^{(k,j)}u_{i}(x,y)=\partial^{k+j} u_{i}(x,y)/\partial x^{k}\partial y^{j}NEWLINE\]NEWLINE with the boundary conditions NEWLINE\[NEWLINEu_1(x_0,y)=\phi_1(y),\;u_2(x_1,y)=\phi_2(y),\;u_1(x,y_1)=\psi_1(x),\;u_2(x,y_0)=\psi_2(x)NEWLINE\]NEWLINE and the consistency conditions \(\phi_1(y_1)=\psi_1(x_0), \phi_2(y_0)=\psi_2(x_1)\).
reviewed by: Aleksandr D. Borisenko
description: scientific article; zbMATH DE number 1631418