The method of Fokas for solving linear partial differential equations
The classical methods for solving initial-boundary-value problems for linear partial
differential equations with constant coefficients rely on separation of variables and specific …
differential equations with constant coefficients rely on separation of variables and specific …
The unified transform for evolution equations on the half‐line with time‐periodic boundary conditions
AS Fokas, MC van der Weele - Studies in Applied Mathematics, 2021 - Wiley Online Library
This paper elaborates on a new approach for solving the generalized Dirichlet‐to‐Neumann
map, in the large time limit, for linear evolution PDEs formulated on the half‐line with time …
map, in the large time limit, for linear evolution PDEs formulated on the half‐line with time …
A numerical implementation of the unified Fokas transform for evolution problems on a finite interval
We present the numerical solution of two-point boundary value problems for a third-order
linear PDE, representing a linear evolution in one space dimension. To our knowledge, the …
linear PDE, representing a linear evolution in one space dimension. To our knowledge, the …
[HTML][HTML] Spatiotemporal variations and risk analysis of Chinese typhoon disasters
F Chen, H Jia, E Du, L Wang, N Wang, A Yang - Sustainability, 2021 - mdpi.com
Typhoons are a product of air-sea interaction, which are often accompanied by high winds,
heavy rains, and storm surges. It is significant to master the characteristics and pattern of …
heavy rains, and storm surges. It is significant to master the characteristics and pattern of …
A hybrid analytical-numerical technique for elliptic PDEs
Recent work has given rise to a novel and simple numerical technique for solving elliptic
boundary value problems formulated in convex polygons in two dimensions. The method …
boundary value problems formulated in convex polygons in two dimensions. The method …
Fokas diagonalization of piecewise constant coefficient linear differential operators on finite intervals and networks
S Aitzhan, S Bhandari, DA Smith - Acta applicandae mathematicae, 2022 - Springer
We describe a new form of diagonalization for linear two point constant coefficient
differential operators with arbitrary linear boundary conditions. Although the diagonalization …
differential operators with arbitrary linear boundary conditions. Although the diagonalization …
[HTML][HTML] Heat conduction on the ring: Interface problems with periodic boundary conditions
NE Sheils, B Deconinck - Applied Mathematics Letters, 2014 - Elsevier
The classical problem of heat conduction in one dimension on a composite ring is
examined. The problem is formulated using the heat equation with periodic boundary …
examined. The problem is formulated using the heat equation with periodic boundary …
Kernel density estimation with linked boundary conditions
Kernel density estimation on a finite interval poses an outstanding challenge because of the
well‐recognized bias at the boundaries of the interval. Motivated by an application in cancer …
well‐recognized bias at the boundaries of the interval. Motivated by an application in cancer …
Interface problems for dispersive equations
NE Sheils and, B Deconinck - Studies in Applied Mathematics, 2015 - Wiley Online Library
The interface problem for the linear Schrödinger equations in one‐dimensional piecewise
homogeneous domains is examined by providing an explicit solution in each domain. The …
homogeneous domains is examined by providing an explicit solution in each domain. The …
Riemann-Hilbert problems, their numerical solution and the computation of nonlinear special functions
TD Trogdon - 2013 - digital.lib.washington.edu
The computation of special functions has important implications throughout engineering and
the physical sciences. Nonlinear special functions include the solutions of integrable partial …
the physical sciences. Nonlinear special functions include the solutions of integrable partial …