"A difference scheme with the optimal weight for the diffusion-convection equation"
Sukhinov A.I., Chistyakov A.E., Sidoryakina V.V., and Protsenko S.V.

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.

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

  • Sukhinov A.I. – Don State Technical University, Faculty of Informatics and Computer Science; pl. Gagarina 1, Rostov-on-Don, 344010, Russia; Dr. Sci., Professor, Head of Department, e-mail: sukhinov@gmail.com
  • Chistyakov A.E. – Don State Technical University, Faculty of Informatics and Computer Science; pl. Gagarina 1, Rostov-on-Don, 344010, Russia; Dr. Sci., Professor, e-mail: cheese_05@mail.ru
  • Sidoryakina V.V. – A.P. Chekhov Taganrog Institute (branch) of Rostov State Economical University; ul. Initsiativnaya 48, Taganrog, 347936, Russia; Ph.D., Associate Professor, e-mail: cvv9@mail.ru
  • Protsenko S.V. – Don State Technical University, Faculty of Informatics and Computer Science; pl. Gagarina 1, Rostov-on-Don, 344010, Russia; Graduate Student, e-mail: rab55555@rambler.ru