Numerical Comparison Between RBF Schemes With Respect to Other Approaches to Solve Fractional Partial Differential Equations and Their Advantages When Choosing Non-Uniform Nodes

Carlos Alberto Torres Martinez¹,, Fernando Brambila Paz²

1. PhD student at Facultad de Ciencias UNAM and professor at Universidad Autonoma de la Ciudad de Mexico (UACM).
2. Proffesor and researcher at Facultad de Ciencias UNAM, Mexico.

Abstract: In this work, some cases of Fractional Partial Differential Equations (FPDE) are considered and resolved numerically using a meshless method via Radial Basis Functions (RBF). Taking different types of fractional derivatives and nonuniform collocation nodes. The results are compared with those obtained by previous works. This type of approach sounds like a good choice to deal with problems in higher dimensions or non-uniform data.

Keywords: Fractional Partial Differential Equation (FPDE), Meshless Methods, Radial Basis Functions (RBF), fractional diffusion-wave equation (DWFE), Numerical solution.

Pages: 85 – 105 | Full PDF Paper