Numerical Integration of Space Fractional Partial Differential Equations Vol 2, Applications from Classical Integer PDEs
Numerical Integration of Space Fractional Partial Differential Equations Vol 2, Applications from Classical Integer PDEs by Younes Salehi, William E. Schiesser - 1st edition 2018 - 1 recurso en línea (XII, 192 páginas) - Synthesis Lectures on Mathematics & Statistics 1938-1751 .
Preface -- Simultaneous SFPDEs -- Two Sided SFPDEs -- Integer to Fractional Extensions -- Authors' Biographies -- Index.
Partial differential equations (PDEs) are one of the most used widely forms of mathematics in science and engineering. PDEs can have partial derivatives with respect to (1) an initial value variable, typically time, and (2) boundary value variables, typically spatial variables. Therefore, two fractional PDEs can be considered, (1) fractional in time (TFPDEs), and (2) fractional in space (SFPDEs). The two volumes are directed to the development and use of SFPDEs, with the discussion divided as:
Various definitions of space fractional derivatives have been proposed. We focus on the Caputo derivative, with occasional reference to the Riemann-Liouville derivative.
In the second volume, the emphasis is on applications of SFPDEs developed mainly through the extension of classical integer PDEs to SFPDEs. The example applications are:
- Fractional diffusion equation with Dirichlet, Neumann and Robin boundary conditions
- Fisher-Kolmogorov SFPDE