Search results for "Computational Mathematic"
showing 10 items of 987 documents
Explicit Bézier control net of a PDE surface
2017
The PDE under study here is a general fourth-order linear elliptic Partial Differential Equation. Having prescribed the boundary control points, we provide the explicit expression of the whole control net of the associated PDE Bézier surface. In other words, we obtain the explicit expressions of the interior control points as linear combinations of free boundary control points. The set of scalar coefficients of these combinations works like a mould for PDE surfaces. Thus, once this mould has been computed for a given degree, real-time manipulation of the resulting surfaces becomes possible by modifying the prescribed information. The work was partially supported by Spanish Ministry of Econo…
Indefinite integrals involving complete elliptic integrals of the third kind
2017
ABSTRACTA method developed recently for obtaining indefinite integrals of functions obeying inhomogeneous second-order linear differential equations has been applied to obtain integrals with respect to the modulus of the complete elliptic integral of the third kind. A formula is derived which gives an integral involving the complete integral of the third kind for every known integral for the complete elliptic integral of the second kind. The formula requires only differentiation and can therefore be applied for any such integral, and it is applied here to almost all such integrals given in the literature. Some additional integrals are derived using the recurrence relations for the complete …
Indefinite integrals of incomplete elliptic integrals from Jacobi elliptic functions
2017
Integration formulas are derived for the three canonical Legendre elliptic integrals. These formulas are obtained from the differential equations satified by these elliptic integrals when the indep...
Indefinite integrals involving the Jacobi Zeta and Heuman Lambda functions
2017
ABSTRACTJacobian elliptic functions are used to obtain formulas for deriving indefinite integrals for the Jacobi Zeta function and Heuman's Lambda function. Only sample results are presented, mostly obtained from powers of the twelve Glaisher elliptic functions. However, this sample includes all such integrals in the literature, together with many new integrals. The method used is based on the differential equations obeyed by these functions when the independent variable is the argument u of elliptic function theory. The same method was used recently, in a companion paper, to derive similar integrals for the three canonical incomplete elliptic integrals.
Stellar hydrodynamics with glaister's riemann solver: An approach to the stellar collapse
1990
La resolution de Remann approximee de la solution des equations d'Euler de la dynamique des gaz 1 D, developpee par Glaister P. (1988, J. Comput. Phys., 74) est introduite dans un code hydrodynamique lagrangien et appliquee a l'effondrement stellaire a symetrie spherique
Systèmes hyperboliques d'équations aux dérivées partielles linéaires : régularité et matrices diagonalisables
2001
Resume La regularite des solutions d'un systeme d'equations aux derivees partielles hyperbolique, est liee aux proprietes spectrales d'un faisceaux de matrices reelles. Nous nous interessons ici a la regularite L 2 . Celle ci est obtenue si et seulement si l'exponentielle imaginaire du faisceau est bornee. Nous regardons le lien entre cette condition et les proprietes spectrales du faisceau, ici diagonalisable sur R . Nous donnons en particulier un critere d'exponentielle bornee si les valeurs propres ne sont pas de multiplicites constantes, et nous montrons que dans le cas des faisceaux engendres par deux matrices 3×3, l'exponentielle est bornee si et seulement si le faisceau est analytiqu…
Further monotonicity and convexity properties of the zeros of cylinder functions
1992
AbstractLet cvk be the kth positive zero of the cylinder function Cv(x,α)=Jv(x) cos α−Yv sin α, 0⩽α<π, where Jv(x) and Yv(x) are the Bessel functions of the first and the second kind, respectively. We prove that the function v(d2cvkddv2+δ)cvk increases with v⩾0 for suitable values of δ and k−απ⩾ 0.7070… . From this result under the same conditions we deduce, among other things, that cvk+12δv2 is convex as a function of v⩾0. Moreover, we show some monotonicity properties of the function c2vkv. Our results improve known results.
Application of Genetic Algorithm on Parameter Optimization of Three Vehicle Crash Scenarios
2017
Abstract This paper focuses on the development of mathematical models for vehicle frontal crashes. The models under consideration are threefold: a vehicle into barrier, vehicle-occupant and vehicle to vehicle frontal crashes. The first model is represented as a simple spring-mass-damper and the second case consists of a double-spring-mass-damper system, whereby the front mass and the rear mass represent the vehicle chassis and the occupant, respectively. The third model consists of a collision of two vehicles represented by two masses moving in opposite directions. The springs and dampers in the models are nonlinear piecewise functions of displacements and velocities respectively. More spec…
Approximate Osher–Solomon schemes for hyperbolic systems
2016
This paper is concerned with a new kind of Riemann solvers for hyperbolic systems, which can be applied both in the conservative and nonconservative cases. In particular, the proposed schemes constitute a simple version of the classical Osher-Solomon Riemann solver, and extend in some sense the schemes proposed in Dumbser and Toro (2011) 19,20. The viscosity matrix of the numerical flux is constructed as a linear combination of functional evaluations of the Jacobian of the flux at several quadrature points. Some families of functions have been proposed to this end: Chebyshev polynomials and rational-type functions. Our schemes have been tested with different initial value Riemann problems f…
Incremental Treatments of the Full Configuration Interaction Problem
2020
The recent many-body expanded full configuration interaction (MBE-FCI) method is reviewed by critically assessing its advantages and drawbacks in the context of contemporary near-exact electronic structure theory. Besides providing a succinct summary of the history of MBE-FCI to date within a generalized and unified theoretical setting, its finer algorithmic details are discussed alongside our optimized computational implementation of the theory. A selected few of the most recent applications of MBE-FCI are revisited, before we close by outlining its future research directions as well as its place among modern near-exact wave function-based methods.