Discrete Artificial Boundary Conditions for the Korteweg-de Vries Equation

TL;DR

This paper develops and analyzes discrete artificial boundary conditions for the linearized KdV equation using Z-transformation, providing numerical benchmarks to demonstrate their effectiveness.

Contribution

It introduces new discrete artificial boundary conditions for the linearized KdV equation based on Z-transformation, enhancing numerical simulation accuracy.

Findings

Effective boundary conditions derived for the linearized KdV equation.

Numerical benchmarks validate the proposed boundary conditions.

Improved stability and accuracy in numerical schemes.

Abstract

In this paper we consider two numerical scheme based on trapezoidal rule in time for the linearized KdV equation in one space dimension. The goal is to derive some suitable artificial boundary conditions for these two full discretization using Z-transformation. We give some numerical benchmark examples from the literature to illustrate our findings.