THE CONVERGENCE AND STABILITY OF EXPLICIT DIFFERENCE SCHEMES FOR NONLINEAR SCHRODINGER EQUATION

The Convergence and Stability of Explicit Difference Schemes for Nonlinear Schr Odinger Equation

Finite Difference Schemes and the Schrodinger Equation

In this paper, we primarily explore numerical solutions to the Quantum 1D Infinite Square Well problem, and the 1D Quantum Scattering problem. We use different finite difference schemes to approximate the second derivative in the 1D Schrodinger’s Equation and linearize the problem. By doing so, we convert the Infinite Well problem to a simple Eigenvalue problem and the Scattering problem to a s...

Numerical Stability of Explicit Runge-Kutta Finite Difference Schemes for the Nonlinear Schrödinger Equation

Article history: Received 8 July 2012 Received in revised form 1 January 2013 Accepted 26 April 2013 Available online 3 May 2013

Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation

In this paper, we consider the variable-order nonlinear fractional diffusion equation ∂u(x, t) ∂t = B(x, t)xR u(x, t) + f(u, x, t), where xR α(x,t) is a generalized Riesz fractional derivative of variable order α(x, t) (1 < α(x, t) ≤ 2) and the nonlinear reaction term f(u, x, t) satisfies the Lipschitz condition |f(u1, x, t) − f(u2, x, t)| ≤ L|u1 − u2|. A new explicit finite difference approxim...

Stability Criterion for Explicit Schemes (Finite-Difference Method) on the Solution of the Advection-Diffusion Equation

The numerical solutions of the advection-diffusion equation are themselves numerous and sometimes very sophisticated, in order to avoid two undesirable features: oscillatory behavior and numerical diffusion. It is known that the common practice of “splitting-up” the solution is not always the best approach to the advection-diffusion problem. By using the ordinary differential equation analogy m...