Abstract
In this chapter, partial differential equations that govern many featured wave propagation phenomena are discussed. We start with modelling the process of string vibration through a partial differential equation, known as the wave equation, or the equation for string vibration. Then the concepts of initial and boundary conditions are introduced. This is followed by the presentation of a number of relevant methods widely used for solving problems governed by the wave equation. Our scope is then extended to cover two-/three-dimensional cases of wave propagation. The chapter concludes with discussion over the properties of solutions for problems governed by the wave equation.
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Zhu, Y. (2021). The Wave Equation. In: Equations and Analytical Tools in Mathematical Physics. Springer, Singapore. https://doi.org/10.1007/978-981-16-5441-1_1
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DOI: https://doi.org/10.1007/978-981-16-5441-1_1
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Publisher Name: Springer, Singapore
Print ISBN: 978-981-16-5440-4
Online ISBN: 978-981-16-5441-1
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