Error estimate for diffusion equations solved by schemes with weights
Tóm tắt
In applied problems it is often necessary to solve the diffusion equation. Here, the most efficient methods are grid methods, but they suffer from errors of approximation. We consider a linear equation of diffusion with variable coefficients, for which the error can be estimated by a scheme with weights. An algorithm is proposed to find the optimal value of the weight for the error in the given grid spacing to be minimal.
Tài liệu tham khảo
V. S. Vladimirov, Equations of Mathematical Physics (Nauka, Moscow, 1971) [in Russian].
A. A. Samarskii, Theory of Difference Schemes (Nauka, Moscow, 1983) [in Russian].
A. I. Sukhinov, Two-Dimensional Schemes of Splitting and Some of Their Applications (MAKS Press, Moscow, 2005) [in Russian].
A. E. Chistyakov, “A three-dimensional model of the motion of water medium in the Azov Sea in view of salt and heat transport,” Izv. SFD Tekhn. Nauk, No. 8 (97), 75–82 (2009).
A. I. Sukhinov, A. E. Chistyakov, and E. V. Alekseyenko, “Numerical implementation of the three-dimensional model of hydrodynamics for shallow water basins in a super-computational system,” Math. Models Comput. Simul. 23(3), 3–21 (2011).
A. A. Samarskii and A. V. Gulin, Numerical Methods (Nauka, Moscow, 1989) [in Russian].
M. E. Ladonkina, O. A. Neklyudova, V. F. Tishkin, and V. S. Chevanin, “On a variant of significantly non-oscillating difference schemes of high order of accuracy for systems of conservation laws,” Math. Models Comput. Simul. 21(11), 19–32 (2009).
M. E. Ladonkina, O. Yu. Milyukova, and V. F. Tishkin, “A numerical method of solving the diffusion type equations based on the multi-grid method,” J. Exp. Theor. Phys. 50(8), 1438–1461 (2010).