Numerical method for Cahn-Hilliard equation has been well-studied, but few can be generalized to fractional Cahn-Hilliard equation. In this project to modified the numerical method proposed by Brian Wetton et al in the paper High accuracy solutions to energy gradient flows from material science models[1]. The method they described in the paper is a pseudo-spectral method suitable for considerin...

The rst part of this thesis concerns the formulation of numerical methods that are local in time for the solution of equations with memory. The main idea is that the solution will be updated in the Fourier domain in order to avoid evaluating time convolution integrals that have memory. This work was made possible by the development of a good quadrature[31] of the Fourier integral where a small ...

The rst part of this thesis concerns the formulation of numerical methods that are local in time for the solution of equations with memory. The main idea is that the solution will be updated in the Fourier domain in order to avoid evaluating time convolution integrals that have memory. This work was made possible by the development of a good quadrature[31] of the Fourier integral where a small ...

We consider a parabolic-type PDE with diffusion given by fractional Laplacian operator and quadratic nonlinearity of the 'gradient' solution, convoluted singular term b. Our first result is well-posedness for this problem: show existence uniqueness (local in time) mild solution. The main about blow-up said particular we find sufficient conditions on initial datum b to ensure solution finite time.

This paper gathers the tools for solving Riemann-Liouville time fractional non-linear PDE’s by using a Galerkin method. method has advantage of not being more complicated than one used to solve same PDE with first order derivative. As model problem, existence and uniqueness is proved semilinear heat equations polynomial growth at infinity.

Based on the local fractional derivative, a new Klein-Fock-Gordon equation is derived in this paper for first time. A simple method namely Yang?s special function used to seek non-differentiable exact solutions. The whole calculation process strongly shows that proposed and effective, can be applied investigate solu?tions of other PDE.

In this present work, we perform a numerical analysis of the value European style options as well sensitivity for option price with respect to some parameters model when underlying process is driven by fractional Lévy process. The given deterministic representation means real valued function satisfying PDE. scheme PDE obtained weighted and shifted Grunwald approximation.

Neural networks with radial basis functions method are used to solve a class of initial boundary value of fractional partial differential equations with variable coefficients on a finite domain. It takes the case where a left-handed or right-handed fractional spatial derivative may be present in the partial differential equations. Convergence of this method will be discussed in the paper. A num...