An O(h6) accurate difference approximation to solutions of the Helmholtz equation is derived. The discrete equations are solved using a reduction procedure and Fourier analysis. Its computational performance is compared with a fourth order similar method over a set of linear and mildly nonlinear...

A finite element formulation is derived for the equation of heat conduction with temperature dependent conductivity and heat capacity. The derivation of the finite element model is based on a variational formulation of the heat conduction equation which, together with generalized coordinates,...

Adaptive grid refinement is potentially a very powerful means of dealing with singularities and other types of misbehavior in the solutions of elliptic partial differential equations. Combined with the multi-level iterative technique for solving the matrix equations, the method can be...

A review of full scale simulation of water distribution systems is made which reveals the computational problems associated with on-line applications. The paper then presents a generalised method for obtaining simplified dynamic models of complex water supply systems. The models obtained have...

In this paper a new, n-body approach is developed for the modeling of liquid phenomena. Both long and short range forces are included. Computer examples of several prototype, nonlinear, free surface problems are described and discussed.