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Showing 1 to 5 of 5 for “"Fokas Method"”.
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Numerical analysis of the Fokas method in two and three dimensions
… called the unified approach of [Fok08], or “Fokas method”. It is hoped that the positive results we present here will motivate further inclusion of the Fokas method in numerical packages.
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Acoustic Scattering by Gratings
… noise reduction metamaterials. The semi-analytic Fokas method is extended to periodic geometries, and the resulting integral equation, recognised as a generalised Dirichlet-to-Neumann map, is solved numerically; the scattering solution is recovered through a Green's integral representation. The …
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Initial and boundary value problems in two and three dimensions
… line. In 1967 the Inverse Scattering Transform method was introduced; this method can be used for the solution of the initial value problem of certain integrable equations including the celebrated Korteweg-de Vries and nonlinear Schrödinger equations. The extension of this method from initial …
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Solution Of Linear Evolution Partial Differential Equations On The Half-Line
… of new techniques, such as the Unified Transform method. Lastly, we examine how the Unified Transform method can be invoked to solve initial boundary value problems involving the linear Schrodinger and Airy equations.
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Boundary Value Problems for the Laplace Equation on Convex Domains with Analytic Boundary
… Following this, we construct a numerical method that uses the global relation to find the Neumann data, given the Dirichlet data, for a given BVP for the Laplace equation on a domain with smooth boundary.