loading page

Anomalous Diffusion Equation Modeled by the Joint Use of Domain Boundary Element Method and Analytical Derived Solution Based on Green Equation
  • +1
  • Kymie Karina Silva Saito,
  • Otto Corrêa Rotunno Filho,
  • Webe João Mansur,
  • jose antônio marques carrer
Kymie Karina Silva Saito
Universidade Federal do Pará

Corresponding Author:kymiesaito@gmail.com

Author Profile
Otto Corrêa Rotunno Filho
Universidade Federal do Rio de Janeiro
Author Profile
Webe João Mansur
Universidade Federal do Rio de Janeiro
Author Profile
jose antônio marques carrer
Universidade Federal do Paraná
Author Profile


Mathematical formulation of the diffusion phenomenon might be described through a differential equation, which takes into account complementary and different effects with respect to the physical processes simulated with the support of the Fick´s equation, which is usually adopted to represent the diffusion process. In particular, diffusion applied to spatio-temporal retention problems with bimodal mass transmission are highlighted. To better understand this physical phenomenon, the proper use of the analytical Green function (GF) or the steady-state fundamental solution was investigated. In this case, we use the Boundary Element Method formulation is presented for the solution of the anomalous diffusion equation for one-dimensional problems. The formulation employs the steady-state fundamental solution. Besides the basic integral equation, another one is required, due to the fourth-order differential operator in the differential equation of the problem. The domain discretization employs linear cells. The first order time derivative is approximated by a backward finite difference scheme. Two examples are presented. Numerical results are compared with analytical solutions, showing good agreement between them.