Development of a numerical phase optimized upwinding combined compact difference scheme for solving the Camassa-Holm equation with different initial solitary waves

• Published in: Numerical methods for partial differential equations Vol. 31; no. 5; pp. 1645 - 1664
• Main Authors: Yu, C. H., Sheu, Tony W. H., Chang, C. H., Liao, S. J.
• Format: Journal Article
• Language: English
• Published: New York Blackwell Publishing Ltd 01.09.2015; Wiley Subscription Services, Inc
• Subjects: Approximation; Camassa-Holm equation; Derivatives; Fluid dynamics; Hamiltonian; Integrity; long-term accurate; Mathematical analysis; Mathematical models; Partial differential equations; upwinding combined compact difference scheme; Wave propagation

In this article, the solution of Camassa–Holm (CH) equation is solved by the proposed two‐step method. In the first step, the sixth‐order spatially accurate upwinding combined compact difference scheme with minimized phase error is developed in a stencil of four points to approximate the first‐order...