FRACTIONAL ORDER FINITE DIFFERENCE SCHEME FOR SPACE FRACTIONAL DIFFUSION EQUATION (286,00 руб.)

UDC 621 FRACTIONAL ORDER FINITE DIFFERENCE SCHEME FOR SPACE FRACTIONAL DIFFUSION EQUATION © K.C. Takale RNC Arts, JDB Commerce and NSC Science College, Nashik-Road, India V.R. Nikam LokneteVyankatrao Hire, Arts Science and Commerce College, Panchvati, Nashik, India S.R. Kulkarni Model College, Dombivali, Thane, India Abstract. <...> The aim of this paper is to develop the fractional order implicit finite difference scheme for space fractional diffusion equation (SFDE) with mixed boundary conditions. <...> As an application of this scheme numerical solution for space fractional diffusion equation is obtained with the help of Mathematica software. <...> The theory of fractional calculus is useful mathematical tool for applied sciences but it is, somehow hard to tackle and become the topic of active research among the researchers. <...> Therefore, we develop the fractional order implicit finite difference scheme for space fractional diffusion equation with homogeneous mixed initial and boundary conditions. <...> We consider the space fractional diffusion equation (SFDE) with mixed initial and boundary conditions: , (1.1) initial condition: , (1.2) 120 Engineering and automation problems, № 3 – 2014 where N is the positive integer, is the gamma function. and boundary conditions: (1.3) where variable coefficient d(x) > 0. <...> We organize this paper as follows: In section 2, the fractional order implicit finite difference scheme is developed for space fractional diffusion equation. <...> Numerical solution of space fractional diffusion equation is obtained and it is simulated by using Mathematica software in the last section. 2. <...> FINITE DIFFERENCE APPROXIMATION FOR SFDE In this section we develop the space fractional order implicit finite difference scheme (SFIFDS) for fractional diffusion equation (FDE) (1.1) – (1.3). <...> We discretize the spatial -order fractional derivative using the Grnwald finite difference formula at all time levels. <...> The standard Grnwald estimates generally yield unstable finite difference equation regardless of whatever the resulting finite difference method is an explicit or an implicit system for related discussion [6]. <...> Therefore, we use a right shifted Grnwald formula to estimate <...>