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Convergence of the Projection Difference Scheme for the Nonlinear Parabolic Equation with Transformed Spatial Argument

Authors :
Razgulin, A.
Roganovich, I.
Source :
Computational Mathematics and Modeling; July 2001, Vol. 12 Issue: 3 p262-270, 9p
Publication Year :
2001

Abstract

We consider a mixed initial boundary-value problem for the nonlinear parabolic functional-differential equation. The functional part of the equation depends on a generalized superposition of the sought solution and a transformation of the one-dimensional spatial argument. An approximate projection difference scheme is proposed for a wide class of measurable (including non-invertible) transformations. An O(τ + h1 + γ) bound is obtained for the rate of convergence in the L2(Q) norm to the generalized solutions of the original problem without prior assumptions about invertibility of the transformation, smoothness of the solution, or compatibility of grid increments.

Details

Language :
English
ISSN :
1046283X and 1573837X
Volume :
12
Issue :
3
Database :
Supplemental Index
Journal :
Computational Mathematics and Modeling
Publication Type :
Periodical
Accession number :
ejs37711857
Full Text :
https://doi.org/10.1023/A:1012549624125