The Method of Fokas for Solving Linear Partial Differential Equations
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Publication:5408234
DOI10.1137/110821871zbMath1295.35002OpenAlexW2053023596MaRDI QIDQ5408234
Thomas Trogdon, Vishal Vasan, Bernard Deconinck
Publication date: 9 April 2014
Published in: SIAM Review (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/110821871
Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) Initial-boundary value problems for linear higher-order PDEs (35G16) Fundamental solutions to PDEs and systems of PDEs with constant coefficients (35E05)
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The time-dependent Schrödinger equation with piecewise constant potentials ⋮ Linear evolution equations on the half-line with dynamic boundary conditions ⋮ Multilayer heat equations and their solutions via oscillating integral transforms ⋮ The Korteweg-de Vries equation on the half-line with Robin and Neumann data in low regularity spaces ⋮ The linear KdV equation with an interface ⋮ A higher dispersion KdV equation on the half-line ⋮ Fundamental solutions of the fractional Fresnel equation in the real half-line ⋮ Initial value problem for the time-dependent linear Schrödinger equation with a point singular potential by the unified transform method ⋮ Fokas’s Unified Transform Method for linear systems ⋮ Dispersion estimates for the boundary integral operator associated with the fourth order Schrödinger equation posed on the half line ⋮ Generalised Dirichlet to Neumann maps for linear dispersive equations on half-line ⋮ The numerical solution of semidiscrete linear evolution problems on the finite interval using the Unified Transform Method ⋮ The Fokas method for the Broer-Kaup system on the half-line ⋮ Boundary behavior for the heat equation on the half‐line ⋮ The Majda-Biello system on the half-line ⋮ The linear Lugiato-Lefever equation with forcing and nonzero periodic or nonperiodic boundary conditions ⋮ Boundary behavior of the solution to the linear Korteweg‐De Vries equation on the half line ⋮ The Korteweg-de Vries equation on an interval ⋮ Well-posedness of the nonlinear Schrödinger equation on the half-plane ⋮ The Fokas method for integrable evolution equations on a time-dependent interval ⋮ The Unified Transform and the Water Wave Problem ⋮ Well-posedness of a higher dispersion KdV equation on the half-line ⋮ A Hybrid Analytical-Numerical Technique for Elliptic PDEs ⋮ Non-homogeneous wave equation on a cone ⋮ The nonlinear Schrödinger equation on the half-line with a Robin boundary condition ⋮ Fokas method for linear boundary value problems involving mixed spatial derivatives ⋮ Eigenvalues for the Laplace operator in the interior of an equilateral triangle ⋮ Accurate solution method for the Maxey–Riley equation, and the effects of Basset history ⋮ The diffusion equation with nonlocal data ⋮ Multilayer diffusion in a composite medium with imperfect contact ⋮ The hyperbolic Ernst equation in a triangular domain ⋮ The hyperbolic Ernst–Maxwell equations in a triangular domain ⋮ Revivals and fractalisation in the linear free space Schrödinger equation ⋮ The nonlinear Schrödinger equation on the half-line ⋮ On the Fokas method for the solution of elliptic problems in both convex and non-convex polygonal domains ⋮ Evolution partial differential equations with discontinuous data ⋮ Fokas diagonalization of piecewise constant coefficient linear differential operators on finite intervals and networks ⋮ Solving the heat equation with variable thermal conductivity ⋮ Interface Problems for Dispersive Equations ⋮ The Neumann and Robin problems for the Korteweg–de Vries equation on the half-line ⋮ Extended water wave systems of Boussinesq equations on a finite interval: theory and numerical analysis ⋮ Heat conduction on the ring: interface problems with periodic boundary conditions ⋮ Time-periodic linear boundary value problems on a finite interval ⋮ Solution to the 1D Stefan problem using the unified transform method
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