finite and boundary element methods have been used by many authors to solve mathematicalphysics problems. however, the coupling of these two methods happens to be more efficient as it combinestheir merits. in this paper, the mathematical analysis of the coupling of finite and boundary element methodsfor the helmholtz equation is presented.

The paper develops the method for construction of the families of particular solutions to the nonlinear Partial Differential Equations (PDE) without relation to the complete integrability. Method is based on the specific link between algebraic matrix equations and PDE. Example of (2+2)-dimensional generalization of Burgers equation is given. PACS numbers: 05.45.-a, 05.45.Yv

The Richards equation is widely used as a model for the flow of water in unsaturated soils. For modelling one-dimensional flow in a homogeneous soil, this equation can be cast in the form of a specific nonlinear partial differential equation with a time derivative and one spatial derivative. This paper is a survey of recent progress in the pure mathematical analysis of this last equation. The e...

The concept of a closed-form solution to the Riccati equation has been given a precise mathematical definition by Kovacic (1986). Furthermore Kovacic also gave an algorithm that can be used to determine the closed-form solutions to the Riccati ordinary differential equation. The Riccati equation plays an important role in the solution to a class of problems in mathematical finance. In this pape...