We address the Korteweg-de Vries equation as an interesting model of high order partial differential equation, and show that using the classical spectral element method, i.e. a high order continuous Galerkin approximation, it is possible to develop satisfactory schemes, in terms of accuracy, computational efficiency, simplicity of implementation and, if required, conservation of the lower invar...

Even though it is not very often admitted, partial functions do play a significant role in many practical applications of deduction systems. Kleene has already given a semantic account of partial functions using three-valued logic decades ago, but there has not been a satisfactory mechanization. Recent years have seen a thorough investigation of the framework of many-valued truth-functional log...

In recent years, many more of the numerical methods were used to solve a wide range of mathematical, physical and engineering problems linear and nonlinear. In this article, we shall use the homotopy perturbation method (HPM) to solve some systems of partial differential equations viz. the systems of coupled Burgers’ equations in oneand twodimensions and the system of Laplace’s equation. This a...

A model is presented that describes the pumping characteristics of St707 getter material, the evaporation rate of antimony, and the resulting partial pressure of Sb within a vacuum chamber. The results show that within the 250-450◦C range, the partial pressure of antimony ranges from 10−7 Pa to 10−2 Pa. In a limiting case where the getter efficiency is tuned to 10, 000 L/s, partial pressures ar...

: : In this paper, we present a new approach to resolve linear weakly-singular partial integro-differential equations by first removing the singularity using Taylor's approximation and transform the given partial integrodifferential equations into an partial differential equation. After that the fourth order compact finite difference scheme and collocation method is presented to obtain system o...

Adding symmetry breaking constraints is one of the oldest ways of breaking variable symmetries for CSPs. For instance, it is well known that all the symmetries for the pigeon hole problem can be removed by ordering the variables. We have generalized this result to all CSPs where the variables are subject to an all different constraint. In such case it is possible to remove all variable symmetri...