Results 61 to 70 of about 5,765 (234)

A New Legendre Spectral Galerkin and Pseudo-Spectral Approximations for Fractional Initial Value Problems

Abstract and Applied Analysis, 2013
We extend the application of the Galerkin method for treating the multiterm fractional differential equations (FDEs) subject to initial conditions. A new shifted Legendre-Galerkin basis is constructed which satisfies exactly the homogeneous initial ...
A. H. Bhrawy, M. A. Alghamdi
doaj   +1 more source

O(1) Computation of Legendre polynomials and Gauss-Legendre nodes and weights for parallel computing [PDF]

, 2012
A self-contained set of algorithms is proposed for the fast evaluation of Legendre polynomials of arbitrary degree and argument is an element of [-1, 1].
Fostier, Jan, Bogaert, Ignace, Michiels, Bart   +2 more
core   +1 more source

Three‐Dimensional Optical Characterization of Magnetostrictive Deformation in Magnomechanical Systems

Laser &Photonics Reviews, EarlyView.
An optical approach is proposed for real‐time and high‐precision detection of the magnetostrictive deformation of an yttrium‐iron‐garnet sphere in three dimensions, based on the deformation induced spatial high‐order modes of the scattered field, postselection, and balanced homodyne detection.
Xiaomin Liu, Jing Zhang, Jie Li, Rongguo Yang, Jiangrui Gao, Tiancai Zhang   +5 more
wiley   +1 more source

DIFFERENTIAL EQUATIONS OF THE FOURTH ORDER WITH ORTHOGONAL POLYNOMIAL SOLUTIONS

Pesquimat, 2014
In this paper we developed conditions for orthogonality of polynomial Solutions of the fourth order differential equations with polynomial coefficients.
Santiago César Rojas Romero
doaj   +1 more source

The Combined Effects of Variable Viscosity and Thermal Conductivity of An Unsteady Casson Fluid Flow Along a Vertical Porous Channel With Convective Cooling Walls, Using the Bivariate Spectral Local Linearization Method

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT This study examines the combined impact of different thermal conductivity and viscosity on unsteady non‐Newtonian Casson fluid flow of incompressible, electrical conductivity in a porous vertical channel with convective cooling walls, uniform magnetic field, and constant pressure gradient.
A. S. Adeyemo, Precious Sibanda, S. P. Goqo   +2 more
wiley   +1 more source

A Novel Optimized Local Linearization Hybrid Block Method for Chaotic Systems: Applications to Stretch‐Twist‐Fold Flow and Bond Orbital Chaotic Attractors

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT The numerical approximation of nonlinear chaotic differential systems, such as the modified stretch‐twist‐fold (STF) flow and multi‐bond chaotic attractors, presents a significant challenge due to their sensitive dependence on initial conditions and complex dynamics where analytical solutions are unattainable.
Shina Daniel Oloniiju, Anastacia Dlamini
wiley   +1 more source

Legendre Polynomials Spectral Approximation for the Infinite-Dimensional Hamiltonian Systems [PDF]

, 2011
This paper considers a Legendre polynomials spectral approximation for the infinite-dimensional Hamiltonian systems. As a consequence, the Legendre polynomials spectral semidiscrete system is a Hamiltonian system for the Hamiltonian system whose ...
Zhongquan Lv, Mei Xue, Yushun Wang
core   +1 more source

Existence of Solution for Two Classes of Quasilinear Systems Defined on a Nonreflexive Orlicz–Sobolev Spaces

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT This paper proves the existence of nontrivial solution for two classes of quasilinear systems of the type −ΔΦ1u=Fu(x,u,v)+λRu(x,u,v)inΩ−ΔΦ2v=−Fv(x,u,v)−λRv(x,u,v)inΩu=v=0on∂Ω$$ \left\{\begin{array}{l}\hfill -{\Delta}_{\Phi_1}u={F}_u\left(x,u,v\right)+\lambda {R}_u\left(x,u,v\right)\kern0.1832424242424242em \mathrm{in}\kern0.3em \Omega ...
Lucas da Silva, Marco Souto
wiley   +1 more source

Option pricing with Legendre polynomials

Journal of Computational and Applied Mathematics, 2017
Here we develop an option pricing method based on Legendre series expansion of the density function. The key insight, relying on the close relation of the characteristic function with the series coefficients, allows to recover the density function rapidly and accurately. Based on this representation for the density function, approximations formulas for
Julien Hok, Tat Lung (Ron) Chan
openaire   +3 more sources

Analysis of the fractional scattering contribution in the forward peak for multicomponent systems

Quarterly Journal of the Royal Meteorological Society, EarlyView.
Derivation and justification of mixing rules for multicomponent systems. A novel formulation of the delta‐Eddington scaling rule. Analytical guidance for comparing radiative transfer results. Abstract The widely used δ‐Eddington approximation improves the accuracy of radiative transfer calculations by representing the fraction of scattering into the ...
Jiangnan Li, Yue Cai
wiley   +1 more source