We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Numerical solution of two‐dimensional nonlinear Riesz space‐fractional reaction–advection–diffusion equation using fast compact implicit integration factor method.
- Authors
Biswas, Chetna; Das, Subir; Singh, Anup; Sadowski, Tomasz
- Abstract
In the present article, a finite domain is considered to find the numerical solution of a two‐dimensional nonlinear fractional‐order partial differential equation (FPDE) with Riesz space fractional derivative (RSFD). Here two types of FPDE–RSFD are considered, the first one is a two‐dimensional nonlinear Riesz space‐fractional reaction–diffusion equation (RSFRDE) and the second one is a two‐dimensional nonlinear Riesz space‐fractional reaction‐advection‐diffusion equation (RSFRADE). SFRDE is obtained by simply replacing second‐order derivative term of the standard nonlinear diffusion equation by the Riesz fractional derivative of order (β+1)∈(1,2)${(\beta +1)}\in (1,2)$ whereas the SFRADE is obtained by replacing the first‐order and second‐order space derivatives from the standard order advection–dispersion equation with the Riesz fractional derivatives of order β∈(0,1)$\beta \in (0,1)$. A numerical method is provided to deal with the RSFD with the weighted and shifted Grünwald–Letnikov (WSGD) approximations, for the spatial discretization. The SFRDE and SFRADE are transformed into a system of ordinary differential equations (ODEs), which have been solved using a fast compact implicit integration factor (FcIIF) with nonuniform time meshes. Finally, the demonstration of the validation and effectiveness of the numerical method is given by considering some existing models.
- Subjects
ADVECTION-diffusion equations; REACTION-diffusion equations; BURGERS' equation; ORDINARY differential equations; PARTIAL differential equations; RIESZ spaces; EQUATIONS
- Publication
ZAMM -- Journal of Applied Mathematics & Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2023, Vol 103, Issue 9, p1
- ISSN
0044-2267
- Publication type
Article
- DOI
10.1002/zamm.202200334