A hybrid analytical–numerical method for solving evolution partial differential equations. I. The half-line

By Natasha Flyer, A. S. Fokas. Proceedings of the Royal Society A, 2008

71 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

The unified method: I. Nonlinearizable problems on the half-line (2011, methodology): “Regarding linear evolution PDEs containing spatial derivatives of second order, the unified method yields novel integral representations which have both analytic and numerical advantages in comparison with the classical integral and series representations: (i) They are uniformly convergent at the bo”
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).”
A numerical implementation of Fokas boundary integral approach: Laplace's equation on a polygonal domain (2011, methodology): “For several dispersive IBV problems, numerical implementations of these integrals have been found to offer opportunities that in some respects improve on previously available techniques (Flyer & Fokas 2008; Fokas 2008; Fokas et al. 2009).”