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Anomalous Diffusion Equation Modeled by the Joint Use of Domain Boundary Element Method and Analytical Derived Solution Based on Green Equation
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  • 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:[email protected]

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