r-Modified Crank-Nicholson difference scheme for fractional parabolic PDE

A Characteristic Difference Scheme for Time-Fractional Heat Equations Based on the Crank-Nicholson Difference Schemes

and Applied Analysis 3 As in the classical Crank-Nicholson difference scheme, we will obtain a discrete approximation to the fractional derivative ∂U t, x /∂t at tn 1/2 , xi . Let H t, x 1 Γ 1 − α ∫ t 0 u s, x − u 0, x t − s α ds. 2.1

Numerical Solution of Fractional Wave Equation using Crank-Nicholson Method

In this paper, Crank-Nicholson method for solving fractional wave equation is considered. The stability and consistency of the method are discussed by means of Greschgorin theorem and using the stability matrix analysis. Numerical solutions of some wave fractional partial differential equation models are presented. The results obtained are compared to exact solutions.

WELL- POSEDNESS OF THE ROTHE DIFFERENCE SCHEME FOR REVERSE PARABOLIC EQUATIONS

Difference-Quadrature Schemes for Nonlinear Degenerate Parabolic Integro-PDE

We derive and analyze monotone difference-quadrature schemes for Bellman equations of controlled Lévy (jump-diffusion) processes. These equations are fully non-linear, degenerate parabolic integro-PDEs interpreted in the sense of viscosity solutions. We propose new “direct” discretizations of the non-local part of the equation that give rise to monotone schemes capable of handling singular Lévy...

Crank-Nicolson Difference Scheme for the Generalized Rosenau-Burgers Equation

In this paper, numerical solution for the generalized Rosenau-Burgers equation is considered and Crank-Nicolson finite difference scheme is proposed. Existence of the solutions for the difference scheme has been shown. Stability, convergence and priori error estimate of the scheme are proved. Numerical results demonstrate that the scheme is efficient and reliable. Keywords—Generalized Rosenau-B...