A New Numerical Simulation for Modified Camassa-Holm and Degasperis-Procesi Equations via Trigonometric Quintic B-spline

Authors : İhsan Çelikkaya

Pages : 143-158

Doi:10.54974/fcmathsci.1398394

View : 26 | Download : 36

Publication Date : 2024-07-31

Article Type : Research Paper

Abstract :In this study, the soliton solutions of the modified Camassa-Holm (mCH) and Degasperis-Procesi (mDP) equations, called modified b-equations with important physical properties, were obtained. The soliton waves\' movement and positions formed by solving the mCH and mDP equations were calculated. Ordinary differential equation systems were obtained using trigonometric quintic B-spline bases for position and time direction derivatives in the equations to obtain numerical solutions. An algebraic equation system was then created by writing Crank-Nicolson type approximations for time and position-dependent terms. The stability analysis of this system was examined using the von-Neumann Fourier series method. L₂, L_{∞} and absolute error norms were used to measure the numerical results\' convergence to the real solution. The numerical results calculated were compared with the exact solution and some studies in the literature.
Keywords : Modified Camassa Holm, Modified Degasperis Procesi Equation, Soliton Waves, Trigonometric Quintic B spline bases, Collocation Method