On stability and convergence of semi-Lagrangian methods for the first-order time-dependent nonlinear partial differential equations in 1D
| Autor: | Daniel X. Guo |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
010504 meteorology & atmospheric sciences
Applied Mathematics Mathematical analysis Numerical methods for ordinary differential equations Explicit and implicit methods 010103 numerical & computational mathematics Exponential integrator 01 natural sciences Stochastic partial differential equation Computational Mathematics Runge–Kutta methods Collocation method 0101 mathematics 0105 earth and related environmental sciences Numerical stability Numerical partial differential equations Mathematics |
| Zdroj: | Journal of Computational and Applied Mathematics. 324:72-84 |
| ISSN: | 0377-0427 |
| DOI: | 10.1016/j.cam.2017.04.022 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect