A new transform method for evolution partial differential equations
By A. S. Fokas. 2002
140 citations recorded by the source corpus.
Subfields: Modeling and Simulation, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/6b733231f7588b6de39aad2010de01fb30b7ce95
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In Modeling and Simulation
- Beatrice Pelloni
- W. Saarloos
- Natasha Flyer
- A. S. Fokas
- Bengt Fornberg
- Anne Boutet de Monvel
- Dmitry Shepelsky
- Wenxiu Ma
In Numerical Analysis
- Beatrice Pelloni
- A. S. Fokas
- Bengt Fornberg
- Anne Boutet de Monvel
- Dmitry Shepelsky
- W. Saarloos
- Natasha Flyer
- Jonatan Lenells
Citations in the corpus
- A hybrid analytical–numerical method for solving evolution partial differential equations. I. The half-line (2008, unknown): “A detailed discussion is given in Fokas (2002).”
- Front propagation into unstable states (2003, methodology): “The “new method” proposed in [164] is essentially a reinvention of parts of the work half a century before in plasma physics and fluid dynamics referenced below, and this paper contains no references to these earlier developments.”
- A numerical implementation of Fokas boundary integral approach: Laplace's equation on a polygonal domain (2011, background): “…a decade ago, Fokas and collaborators introduced a new analytical transform technique that provides closed-form solutions (in terms of contour integrals) for a variety of PDE boundary value (BV) and initial-boundary value (IBV) problems (Fokas 1997, 2001, 2002, Fokas & Pelloni 2005; Spence 2010).”
- The spectral representation of two-point boundary-value problems for third-order linear evolution partial differential equations (2005, methodology): “The important result of Fokas & Pelloni (2005) implies that the analysis of this single equation yields an explicit representation for the spectral functions ~ f ðt; kÞ and ~ gðt; kÞ in terms of q0(x) and the given boundary conditions only.”
- Analysis of the Global Relation for the Nonlinear Schrödinger Equation on the Half-line (2003, result): “Remark 2. Suppose that qðx; tÞ satisfies the linearized Schro¨ dinger equation iqt þ qxx ¼ 0. In this case the global relation is ([ 4 ])”