We consider parameter dependent semilinear evolution problems for which, at the limit value of the parameter, the problem is finite dimensional. We introduce an abstract functional analytic framework that applies to many problems in the existing literature for which the study of the asymptotic dynamics can be reduced to finite dimensions via the invariant manifold theory. Some practical models ...

We present an explicit finite-difference scheme for direct simulation of the motion of solid particles in a fluid. The method is based on a second order MacCormack finite-difference solver for the flow, and Newton’s equations for the particles. The fluid is modeled with fully compressible mass and momentum balances; the technique is intended to be used at moderate particle Reynolds number. Seve...

Implicit finite difference schemes for the 3-D wave equation using a 27-point stencil on the cubic grid are presented, for use in room acoustics modelling and artificial reverberation. The system of equations that arises from the implicit formulation is solved using the Jacobi iterative method. Numerical dispersion is analysed and computational efficiency is compared to second-order accurate 27...

The unit-derived method in coding theory is shown to be a unique optimal scheme for constructing and analysing codes. In many cases efficient and practical decoding methods are produced. Codes with efficient decoding algorithms at maximal distances possible are derived from unit schemes. In particular unit-derived codes from Vandermonde or Fourier matrices are particularly commendable giving ri...

Tube Hydroforming (THF) is getting an increasing amount of attention in industry. THF has advantages such as weight reduction, high dimensional accuracy, and high rigidity. However, this forming process requires precise control of internal pressure and axial feeding. Additionally, in most cases prebending processes must be performed on the tubes before the hydroforming process can be carried ou...

The paper demonstrates advantages of using implicit finite differences for fast, accurate, and reliable differentiating and filtering of multidimensional signals defined on regular grids. In particular, applications to image enhancement and edge detection problems are considered. The theoretical contribution of the paper is threefold. The first adapts the Fourier-Padé-Galerkin approximations ap...

Keywords: Optimized scheme Explicit finite-difference Numerical dispersion Maximum norm Simulated annealing algorithm a b s t r a c t Conventional explicit finite-difference methods have difficulties in handling high-frequency components due to strong numerical dispersions. One can reduce the numerical dispersions by optimizing the constant coefficients of the finite-difference operator. Differ...