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