Numerical method of value boundary problem decision for 2d equation of heat conductivity with fractional derivatives

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki

Vetlugin D Beybalaev¹  Mumina R Shabanova² 

[1] Daghestan State University;Institute of Geothermy Problems, Dagestan Research Center of RAS;

关键词: numerical methods;    stability;    approximation of fractional derivatives;    fractional differential equations;   

DOI  :  

来源: DOAJ

【 摘 要 】

In this work a solution is obtained for the boundary problem for two-dimensional thermal conductivity equation with derivatives of fractional order on time and space variables by grid method. Explicit and implicit difference schemes are developed. Stability criteria of these difference schemes are proven. It is shown that approximation order-by time equal but by space variables it equal two. A solution method is suggested using fractional steps. It is proved that the transition module, corresponding to two half-steps, approximates the transition module for given equation.

【 授权许可】

Unknown