تعداد نشریات | 418 |
تعداد شمارهها | 10,005 |
تعداد مقالات | 83,629 |
تعداد مشاهده مقاله | 78,549,989 |
تعداد دریافت فایل اصل مقاله | 55,683,550 |
A Second-Order Accurate Numerical Approximation for Two-Sided Fractional Boundary Value Advection-Diffusion Problem | ||
Theory of Approximation and Applications | ||
مقاله 8، دوره 13، شماره 1، مرداد 2019، صفحه 119-135 | ||
نوع مقاله: Research Articles | ||
نویسندگان | ||
Elyas Shivanian* 1؛ Hamid Reza Khodabandehlo2 | ||
1Department of Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran | ||
2Department of Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran | ||
چکیده | ||
Fractional order partial differential equations are generalization of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial-boundary value fractional partial differential equations with variable coefficients on a finite domain. An approach based on the classical Crank-Nicolson method combined with spatial extrapolation is used to obtain temporally and spatially second-order accurate numerical estimates. Stability, consistency, and convergence of the method are examined. It is shown that the fractional Crank-Nicolson method based on the shifted Gr"{u}nwald formula is unconditionally stable. Some numerical examples are presented and compared with the exact analytical solution for its order of convergence. Fractional order partial differential equations are generalization of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial-boundary value fractional partial differential equations with variable coefficients on a finite domain. An approach based on the classical Crank-Nicolson method combined with spatial extrapolation is used to obtain temporally and spatially second-order accurate numerical estimates. Stability, consistency, and convergence of the method are examined. It is shown that the fractional Crank-Nicolson method based on the shifted Gr"{u}nwald formula is unconditionally stable. Some numerical examples are presented and compared with the exact analytical solution for its order of convergence. | ||
کلیدواژهها | ||
Numerical fractional PDE؛ Two-sided fractional partial differential equation؛ Shifted Gr"{u}nwald-Letnikov formula؛ Fractional diffusion؛ Crank-Nicolson method | ||
آمار تعداد مشاهده مقاله: 254 |