2024/10/08 by Qiming Wu, Wu, Qiming
Computer Science · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #FOS: Mathematics #Numerical Analysis (math.NA) #Seismology and Earthquake Studies
paper · pdf · doi:10.48550/arxiv.2410.06240
openalex publication_date 2024/10/08 · openalex created_date 2024/10/12 · openalex updated_date 2026/07/28
The Korteweg-de Vries (KdV) equation is a fundamental partial differential equation that models wave propagation in shallow water and other dispersive media. Accurately solving the KdV equation is essential for understanding wave dynamics in physics and engineering applications. This project focuses on implementing the Crank-Nicolson scheme, a finite difference method known for its stability and accuracy, to solve the KdV equation. The Crank-Nicolson scheme's implicit nature allows for a more stable numerical solution, especially in handling the dispersive and nonlinear terms of the KdV equation. We investigate the performance of the scheme through various test cases, analyzing its convergence and error behavior. The results demonstrate that the Crank-Nicolson method provides a robust approach for solving the KdV equation, with improved accuracy over traditional explicit methods. Code is available at the end of the paper.