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.
Leonavičienė, T., Bugajev, A., Jankevičiūtė, G., & Čiegis, R. (2016). On Stability Analysis of Finite Difference Schemes for Generalized Kuramoto-Tsuzuki Equation with Nonlocal Boundary Conditions. Mathematical Modelling and Analysis, 21(5), 630-643. https://doi.org/10.3846/13926292.2016.1198836
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