The classical methods for solving initial-boundary-value problems for linear partial
differential equations with constant coefficients rely on separation of variables and specific …

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 …

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 …

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 …

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 …

We describe a new form of diagonalization for linear two point constant coefficient
differential operators with arbitrary linear boundary conditions. Although the diagonalization …

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 …

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 …

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 …

The computation of special functions has important implications throughout engineering and
the physical sciences. Nonlinear special functions include the solutions of integrable partial …