A Unified Approach To Boundary Value Problems

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The Exponentially Convergent Trapezoidal Rule (2014, methodology): “We focus on eight areas of application, from Cauchy integrals in complex analysis to the solution of integral equations and time-dependent PDEs (sections 12–19).”
Initial-boundary value problems for the coupled modified Korteweg-de Vries equation on the interval (2018, methodology): “In 1997, Fokas [7] (also see [8, 9]) introduced a new method, the so-called Fokas method, for analyzing boundary value problems for linear and for integrable nonlinear PDEs.”
A numerical implementation of Fokas boundary integral approach: Laplace's equation on a polygonal domain (2011, methodology): “We recall that most previous numerical implementations of this new analytic formulation have been limited to a relatively low O(N−2) algebraic rate of convergence [10, 11, 12].”
A Robust Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation (2017, result): “The sort of reasoning illustrated in this figure is similar to that used to study mixed initial-boundary value problems using the unified transform method; see [19, 20].”
The unified method: I. Nonlinearizable problems on the half-line (2011, methodology): “Introduction A unified method for analyzing boundary value problems, extending ideas of the so-called inverse scattering transform method, was introduced in [29, 30, 38].”