The Linear KdV Equation with an Interface
- B. Deconinck, N. Sheils, David A. Smith
- Mathematics
- 14 August 2015
The interface problem for the linear Korteweg–de Vries (KdV) equation in one-dimensional piecewise homogeneous domains is examined by constructing an explicit solution in each domain. The location of…
Well-posed two-point initial-boundary value problems with arbitrary boundary conditions
- David A. Smith
- MathematicsMathematical Proceedings of the Cambridge…
- 29 April 2011
Abstract We study initial-boundary value problems for linear evolution equations of arbitrary spatial order, subject to arbitrary linear boundary conditions and posed on a rectangular 1-space, 1-time…
The diffusion equation with nonlocal data
- P. Miller, David A. Smith
- MathematicsJournal of Mathematical Analysis and Applications
- 3 August 2017
Linear Dispersive Shocks
- David A. Smith, T. Trogdon, V. Vasan
- Mathematics
- 23 August 2019
We present a linear dispersive partial differential equation which manifests a number of qualitative features of dispersive shocks, typically thought to occur only in nonlinear models. The model…
Fokas Diagonalization of Piecewise Constant Coefficient Linear Differential Operators on Finite Intervals and Networks
- Sultan Aitzhan, Sambhav Bhandari, David A. Smith
- MathematicsActa Applicandae Mathematicae - An International…
- 10 December 2020
We describe a new form of diagonalization for linear two point constant coefficient differential operators with arbitrary linear boundary conditions. Although the diagonalization is in a weaker sense…
A numerical implementation of the unified Fokas transform for evolution problems on a finite interval
- E. Kesici, B. Pelloni, T. Pryer, David A. Smith
- Mathematics, Computer ScienceEuropean journal of applied mathematics
- 14 October 2016
This work evaluates the novel solution representation formula obtained by the unified transform, also known as Fokas transform, representing a linear evolution in one space dimension, and formulate a strategy to implement effectively this deformation, which allows for accurate numerical results.
Nonlocal and Multipoint Boundary Value Problems for Linear Evolution Equations
- B. Pelloni, David A. Smith
- Mathematics
- 23 November 2015
We derive the solution representation for a large class of nonlocal boundary value problems for linear evolution partial differential equations (PDE) with constant coefficients in one space variable.…
Evolution PDEs and augmented eigenfunctions. Half-line
- B. Pelloni, David A. Smith
- Mathematics
- 15 August 2014
The solution of an initial-boundary value problem for a linear evolution partial differential equation posed on the half-line can be represented in terms of an integral in the complex (spectral)…
Evolution PDEs and augmented eigenfunctions. Finite interval
- David A. Smith, A. Fokas
- MathematicsAdvances in Differential Equations
- 9 March 2013
The so-called unified method expresses the solution of an initial-boundary value problem (IBVP) for an evolution PDE in the finite interval in terms of an integral in the complex Fourier (spectral)…
The unified transform method for linear initial-boundary value problems: a spectral interpretation
- David A. Smith
- Mathematics
- 15 August 2014
AbstractIt is known that the uni ed transform method may be used to solve any well-posed initial-boundary value problem for a linear constant-coecient evolution equation on the nite in-terval or the…
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