Work

Difference Schemes For Convection-diffusion Equations With Generalized Solutions

Year: 2026

Type: article

Abstract: High-accuracy difference schemes are proposed for a multidimensional convection-diffusion equation in classes of generalized solutions. The piecewise polynomial finite element method is used to approximate spatial variables and the resulting Cauchy problem for a system of ordinary differential equations. As a result, third-order accuracy schemes with respect to spatial variables and fourth-order accuracy schemes with respect to time are obtained. Stability conditions and a priori estimates for the solution of the scheme in classes of nonsmooth solutions are obtained. Based on a special technique, convergence theorems were established in a weaker functional norm. Convergence and accuracy theorems are proven.

Source: Gulf Journal of Mathematics

DOI: 10.56947/sk5b5h94

Authors: Dauletbay Utebaev, Bakhadir Utebaev, Sapura Kalmuratova, Rauaj Djumamuratov

Institutions: Academy of Sciences Republic of Uzbekistan, Karakalpak State University

Language: English

Topic: Singular Perturbation, Asymptotics and Difference Schemes

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W7201874672

FWCI:

Cites: 15

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Related to: 10