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Let's consider the one-dimensional string first. Standard text-book physics considers the three usual boundary conditions here, namely Dirichlet (endpoints of the string are fixed), Neumann (endpoints are free) and Robin conditions (obtained e.g. when the endpoints are attached to a spring). Now, for real sonic propagation, those boundary conditions won't ...


4

Ok, here comes the answer promised in the comment section. Let's start the other way round. In grid methods, one basically selects a number of $N+1$ gridpoints $\{x_k\}_{k=0}^{N}$. As basis functions, one can use Lagrange polynomials constructed over these nodes, each one having polynomial order $N$. For this setup, using Newton-Cotes-like quadrature weights ...


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