On stability and convergence of semi-Lagrangian methods for the first-order time-dependent nonlinear partial differential equations in 1D

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:324

Article

Guo, Daniel X.¹ 

[1] Univ North Carolina Wilmington, Dept Math & Stat, Wilmington, NC 28403 USA

关键词: Semi-Lagrangian methods;    Trajectory;    Runge-Kutta method;    Time-dependent nonlinear partial differential equations;    Explicit and implicit methods;   

DOI  :  10.1016/j.cam.2017.04.022

来源: Elsevier

【 摘 要 】

In this article, one-step semi-Lagrangian method is investigated for computing the numerical solutions of the first-order time-dependent nonlinear partial differential equations in 1D with initial and boundary conditions. This method is based on Lagrangian trajectory or the integration from the departure points to the arrival points (regular nodes) and Runge-Kutta method for ordinary differential equations. The departure points are traced back from the arrival points along the trajectory of the path. The convergence and stability are studied for the implicit and explicit methods. The numerical examples show that those methods work very efficient for the time-dependent nonlinear partial differential equations. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free