On Stability Analysis of Finite Difference Schemes for Generalized Kuramoto-Tsuzuki Equation with Nonlocal Boundary Conditions

Abstract

A general methodology for the stability analysis of discrete approximations of nonstationary PDEs is applied to solve the Kuramoto-Tsuzuki equation, including also the Schr¨odinger problem. Stability regions are constructed for the explicit, backward and symmetrical Euler schemes. The obtained results are applied to solve the Kuramoto-Tsuzuki problem with a non-local integral boundary condition. Results of computational experiments are provided.

Keywords

• finite difference method
• stability analysis
• Kuramoto-Tsuzuki equation
• nonlocal boundary conditions