Summation-by-parts (SBP) operators are finite-difference operators that mimic integration by parts. The SBP operator definition includes a weight matrix that is used formally for discrete integration; however, the accuracy of the weight matrix as a quadrature rule is not explicitly part of the SBP definition. We show that SBP weight matrices are related to trapezoid rules with end corrections w...

Starting with divided di erences of binomial coe cients, a class of multivalued polynomials (three parameters), which includes Bernoulli and Stirling polynomials and various generalizations, is developed. These carry a natural and convenient combinatorial interpretation. Some particular calculations are done and several factorization results are proven and conjectured.

In [2] Bradfield found a link between finite differences formed by Σ2 sets and the mu-arithmetic introduced by Lubarski [10]. We extend this approach into the transfinite: in allowing countable disjunctions we show that this kind of extended mu-calculus matches neatly to the transfinite difference hierarchy of Σ2 sets. The difference hierarchy is intimately related to parity games. When passing...

Abstract– In this paper, structures transformable to regular forms are studied. Here, two cases are investigated. In the first case, the effect of different boundary conditions on these structures are explored, and in the second case the effect of adding or removing members and nodes are studied. In some structures the graph model is regular and different boundary conditions change the correspo...

This paper compares the computational performance of two numerical methods for two models of Transient Flow. One model was defined by method of the Eulerian based expressed in a method of characteristics “MOC”, finite difference form. The other model was defined by method of Regression. Each method was encoded into an existing hydraulic simulation model. Results indicated that the accuracy of t...

The method of multiscale analysis is constructed for dicrete systems of evolution equations for which the problem is that of the far behavior of an input boundary datum. Discrete slow space variables are introduced in a general setting and the related finite differences are constructed. The method is applied to a series of representative examples: the Toda lattice, the nonlinear Klein-Gordon ch...

Abstract. Center manifold and normal form theories as well as numerical simulations are employed to analyse the bifurcation and stability of a 13-dimensional deterministic model associated with the transmission dynamics of two diseases within a host population. The stability of the multiple equilibrium solutions together with the associated possible critical points are discussed. It is shown th...

Numerical solutions to fractional differential equations can be extremely computationally intensive due to the effect of non-local derivatives in which all previous time points contribute to the current iteration. In finite difference methods this has been approximated using the ’short memory effect’ where it is assumed that previous events prior to some certain time point are insignificant and...

Wave-based methods are increasingly viewed as necessary alternatives to geometric methods for room acoustics simulations, as they naturally capture wave phenomena like diffraction and interference. For methods that simulate the three-dimensional wave equation—and thus solve for the entire acoustic field in an enclosed space—computational costs can be high, so efficient algorithms are critical. ...