We examine the use of orthogonal spline collocation for the semi-discretization of the cubic Schrr odinger equation and the two-dimensional parabolic equation of Tappert. In each case, an optimal order L 2 estimate of the error in the semidiscrete approximation is derived. For the cubic Schrr odinger equation, we present the results of numerical experiments in which the integration in time is p...

The aim of this paper is to introduce and solve the generalized radical cubic functional equation related to quadratic functional equation$$fleft(sqrt[3]{ax^{3}+by^{3}}right)+fleft(sqrt[3]{ax^{3}-by^{3}}right)=2a^{2}f(x)+2b^{2}f(y),;; x,yinmathbb{R},$$for a mapping $f$ from $mathbb{R}$ into a vector space. We also investigate some stability and hyperstability results for...

We develop the formal connection of the field theoretical Bethe-Salpeter equation including the ladder approximation with its representation on the light-front for a bosonic model. We use the light-front Green's function for the N-particle system for two-particles plus N-2 intermediate bosons. We derive an infinite set of coupled hierarchy equations or iterated resolvents from which the Green's...

a new simple model is introduced for a liquid and an equation of state is derived based on this model and the statistical mechanical calculations. this equation of state works well for the non-polar and slightly polar liquids. the important conclusion that may be deduced from this equation of state is that if the reduced variables of state are chosen and defined appropriately, then, the princip...

To supply biodiesel with the quality levels required by the standards for alternative fuels, the separation and purification units are extremely important in the biodiesel production plants. The correct knowledge and description of the phase equilibria in systems composed by transesterification products is essential for a correct operation and optimization of the purification process. For that ...

Alexander F. Goncharov,1,2 Jonathan C. Crowhurst,2 John K. Dewhurst,3 Sangeeta Sharma,4 Chrystele Sanloup,5 Eugene Gregoryanz,1,6 Nicolas Guignot,7 and Mohamed Mezouar7 1Geophysical Laboratory, Carnegie Institution of Washington, 5251 Broad Branch Road NW, Washington, DC 20015, USA 2Lawrence Livermore National Laboratory, University of California, 7000 East Avenue, Livermore, California 94551, ...

The reliable prediction of phase stability is a challenging computational problem in chemical process simulation, optimization and design. The phase stability problem can be formulated either as a minimization problem or as an equivalent nonlinear equation solving problem. Conventional solution methods are initialization dependent, and may fail by converging to trivial or non-physical solutions...

The divergent Rayleigh-Schrr odinger perturbation expansions for energy eigenvalues of cubic, quartic, sextic and octic oscillators are summed using algebraic approximants. These approximants are generalized Pad e approximants that are obtained from an algebraic equation of arbitrary degree. Numerical results indicate that given enough terms in the asymptotic expansion the rate of convergence o...