Solutions for some vibrating string problems

• Main Author: Neo, Boon Swee
• Other Authors: Ang Whye-Teong
• Format: Final Year Project
• Language: English
• Published: Nanyang Technological University 2023
• Subjects: Engineering::Mechanical engineering
• Online Access: https://hdl.handle.net/10356/166880
• Institution: Nanyang Technological University

The purpose of this research is to look at numerical approaches and energy concerns for solving initial boundary value problems (IBVPs) with vibrating strings. The study is structured into four sections, beginning with the spectral collocation method for solving linear second-order partial differential equations with varied boundary conditions. After that, energy considerations for the Cauchy-Navier equation of elastodynamic waves are examined. The study then investigates two alternative numerical approaches, the Fourier pseudospectral collocation method and the quartic B-spline collocation method, for solving the Ostrovsky problem, a non-linear wave equation, for the propagation of long waves in shallow water. Lastly, the study delves into the numerical solutions to the Ostrovsky equation and the conservation of energy. The purpose of this paper is to help in the development of more efficient and accurate numerical algorithms for solving IBVPs with vibrating strings.