Radial Basis Functions Generated Finite-Difference Method for the Korteweg-de Vries Equation
American Mathematical Society (AMS) Sectional Meeting at Ohio State University
American Mathematical Society (AMS) Sectional Meeting
Ohio State University
March 16-18, 2018
The Korteweg-de Vries equation (KDV) is a third order non-linear Partial Differential Equation(PDE) which solutions are traveling waves called solitons. A numerical method namely radial basis functions generated finite-difference (RBF-FD) integrating factor method was applied and the numerical solutions of the KDV equations were compared with the analytical solutions for 1, 2 and 3 solitons . Hyperviscosity was used for stability of the RBF-FD method in the case of irregular nodes.
Kabre, Julienne and Reeger, Jonah A., "Radial Basis Functions Generated Finite-Difference Method for the Korteweg-de Vries Equation" (2018). Mathematics Faculty Proceedings, Presentations, Speeches, Lectures. 432.