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In this paper we study the application of boundary integral equation methods to the solution of the Helmholtz equation in a locally perturbed half–plane with Robin or impedance boundary conditions. This problem models outdoor noise propagation from a cutting onto a surrounding flat plane, and also the harbour resonance problem in coastal engineering. We… (More)
We introduce a robust and efficient methodology to solve the Ornstein-Zernike integral equation using the pseudoarc length (PAL) continuation method that reformulates the integral equation in an equivalent but nonstandard form. This enables the computation of solutions in regions where the compressibility experiences large changes or where the existence of… (More)
We consider a class of degenerate diffusion equations where the nonlinearity is assumed to be singular (non-Lipschitz) at zero. It is shown that solutions with compactly supported initial data become identically zero in finite time. Such extinction follows by comparison with newly constructed finite travelling waves connecting two stable equilibria.
This paper describes an original numerical prediction technique developed for the analysis of coupled vibro-acoustic problems in fluid waveguides. Specifically it is a wave-based method that adopts a spectral element approach. Unlike the conventional element-based methods, this technique uses wave functions that satisfy the governing equations to describe… (More)
We study the codimension-one and-two bifurcations of the Ornstein–Zernike equation with hypernetted chain (HNC) closure with Lennard–Jones intermolecular interaction potential. The main purpose of the paper is to present the results of a numerical study undertaken using a suite of algorithms implemented in MATLAB and based on pseudo arc-length continuation… (More)