It is well known that the trapezoidal rule converges geometrically when applied to analytic
functions on periodic intervals or the real line. The mathematics and history of this …

Considered here is a class of Boussinesq systems of Nwogu type. Such systems describe
propagation of nonlinear and dispersive water waves of significant interest such as solitary …

A recently discovered transform approach allows a large class of PDEs to be solved in terms
of boundary and/or contour integrals. We introduce here a spectrally accurate numerical …

There exists a growing literature on using the Fokas method (unified transform method) to
solve Laplace and Helmholtz problems on convex polygonal domains. We show here that …

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 …

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 …

Abstract Newell-Whitehead-Segel (NWS) equation is a nonlinear partial differential equation
used in modeling various phenomena arising in fluid mechanics. In recent years, various …

Integral representations for the solution of linear elliptic partial differential equations (PDEs)
can be obtained using Green's theorem. However, these representations involve both the …

We provide the first significant extension of the unified transform (also known as the Fokas
method) applied to elliptic boundary value problems, namely, we extend the method to …

The linearization of the classical Boussinesq system is solved explicitly in the case of
nonzero boundary conditions on the half‐line. The analysis relies on the unified transform …