DOI: https://doi.org/10.26089/NumMet.v20r325

A difference scheme with the optimal weight for the diffusion-convection equation

Authors

  • A.I. Sukhinov
  • A.E. Chistyakov
  • V.V. Sidoryakina
  • S.V. Protsenko

Keywords:

diffusion-convection equation
difference scheme with weights
optimal value of the weight parameter
approximation error
solution accuracy

Abstract

A difference scheme with weights for a homogeneous spatially one-dimensional diffusion-convection equation is studied. An analysis of the approximation error for the difference scheme as a time step function is performed on the basis of the expansion of the solution and approximation error in a trigonometric basis. An algorithm is proposed to find the optimal weight value that ensures the minimum approximation error of the solution to an initial boundary value problem for given values of the time grid steps. A better accuracy of the constructed scheme with the optimal weight compared to the explicit scheme as well as the efficiency of the algorithm for finding the optimal weight value is shown using a test problem.

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Published

2019-08-05

Issue

Vol. 20 (2019): Issue 3.

Section

Section 1. Numerical methods and applications

Author Biographies

A.I. Sukhinov

Don State Technical University
• Professor

A.E. Chistyakov

Don State Technical University
• Professor

V.V. Sidoryakina

A.P. Chekhov Taganrog Institute
• Associate Professor

S.V. Protsenko

Don State Technical University
• PhD Student

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