## 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… Expand

## 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… Expand

## 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… Expand

## 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… Expand

## 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

## 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.… Expand

## 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)… Expand

## 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)… Expand

## 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… Expand

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