Template-Type: ReDIF-Article 1.0
Author-Name:Arshed Ali,Raza Ali Khan,Imtiaz Ahmad
Author-Email:arshad.ali@icp.edu.pk
Author-Workplace-Name:Department of mathematics, Islamia College Peshawar, Pakistan, Institue  of  Informatics  and  Computing  in  Energy  (IICE), UniversityTenaga  Nasional (UNITEN), Kajang, Selangor, Malaysia
Title:A Computational Simulation of Fractional Advection-Diffusion Model Using Differential Quadrature and Local Radial Basis Functions
Abstract:This articlepresents a local radial basis function-based differential quadrature method for  solving  the  time-fractional  advection-diffusion  equation.  Backward  difference formula   is   utilized   to   approximate   Caputo   fractional   derivative.   Differential quadrature  approach  is  employed  to  compute  the  space  derivatives  by  3-point  central scheme  in  the  neighborhood  of  a  node.  Two  types  of  radial  basis  functions  are  utilized  in numerical  simulations. Accuracy  and  computational  efficiency  of  proposed  technique  is assessed  via 𝐿∞, 𝐿2error  norms,  fractional  order,  time  and  spatial  step  sizes,  rate  of convergence  and  execution  time. Three  nonhomogeneous  test  problems  are  solved  to validate  the  method,  and  the  results  are  compared  with  finite  volume  method  to  show  its superiority.
Keywords:Caputo  fractional  derivative,  Radial  basis  functions,  Fractional  Advection-Diffusion equation, Differential quadrature, Backward difference formula
Journal:International Journal of Innovations in Science and Technology
Pages:926-938
Volume:7
Issue:2
Year:2025
Month:May
File-URL:https://journal.50sea.com/index.php/IJIST/article/view/1362/1907
File-Format: Application/pdf
File-URL:https://journal.50sea.com/index.php/IJIST/article/view/1362
File-Format: text/html
Handle: RePEc:abq:IJIST:v:7:y:2025:i:2:p:926-938