نویسندگان | سارا حاجی علوزرنق,فاطمه ذبیحی |
---|---|
نشریه | Boundary Value Problems |
ضریب تاثیر (IF) | ثبت نشده |
نوع مقاله | Full Paper |
تاریخ انتشار | 2025-07-07 |
رتبه نشریه | علمی - پژوهشی |
نوع نشریه | الکترونیکی |
کشور محل چاپ | ایران |
نمایه نشریه | JCR ,SCOPUS |
چکیده مقاله
This study presents a local meshless method based on radial basis functions for the numerical solution of the non-linear time-fractional Burgers' equation (TFBE) involving the fractional derivatives of Caputo (CFD), and Caputo-Fabrizio (CFFD). Time is discretized using the implicit finite difference scheme with $\theta= 1$, while radial basis functions (RBFs), which do not require a mesh to approximate the solution, are used for spatial discretization. Rubin–Graves technique is used to linearize non-linear terms. Approximation of existing spatial derivatives is done using central and finite difference methods and the temporal derivatives are approximated by using the definition of the Caputo and Caputo-Fabrizio derivatives. With the mentioned techniques, a system of algebraic equations is established. By comparing the results obtained from solving this system with the previous results, it is clear that the presented technique provides accurate, stable, and convergent results.
tags: Fractional partial differential equations, Burgers’ equation, Caputo, Caputo-Fabrizio, Meshless method, Radial basis functions, Collocation method, Finite difference scheme, Rubin–Graves technique.