Department of Mathematics and Statistics
University of North Carolina at Wilmington
Wilmington, NC 28403, USA
email: guod@uncw.edu
Daniel X. Guo
Abstract:
In this article, we study one-step Semi-Lagrangian forward method for
computing the numerical solutions of time-dependent nonlinear partial differential
equations with initial and boundary conditions in one space dimension.
Comparing with classic Semi-Lagrangian method, this method is more
straight forward to analyze and implement.
This method is based on Lagrangian trajectory from the departure points
(regular nodes) to the arrival points by Runge-Kutta methods.
The arrival points are traced forward
from the departure points along the trajectory of the path.
Most likely the arrival points are not on the regular grid nodes.
However, it is convenient to approximate the
high order derivative terms in spatial dimension on regular nodes.
The convergence and stability are studied for the explicit methods.
The numerical examples show that those methods work very efficient for the
time-dependent nonlinear partial differential equations.
Published August 25, 2022.
Math Subject Classifications: 35Q35, 65M12, 76M20.
Key Words: Semi-Lagrangian forward methods; trajectory; Runge-Kutta method;
time-dependent nonlinear partial differential equations.
DOI: https://doi.org/10.58997/ejde.conf.26.g1
Show me the PDF file (423 K), TEX file for this article.
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Daniel Guo Department of Mathematics and Statistics University of North Carolina at Wilmington Wilmington, NC 28403, USA email: guod@uncw.edu |
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