A new method for computing a solution of the Cauchy problem with polynomial data for the system of crystal optics

被引：2

作者：

Yakhno, V. ^{[1
]}

Altunkaynak, M. ^{[2
]}

机构：

[1] Dokuz Eylul Univ, Dept Elect & Elect Engn, Izmir, Turkey

[2] Dokuz Eylul Univ, Dept Math, Izmir, Turkey

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2010年 / 87卷 / 07期

关键词：

analytical method; system of crystal optics; initial value problem; polynomial solutions; symbolic computations; symmetric hyperbolic system;

D O I：

10.1080/00207160802380926

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A new analytical method for solving an initial value problem (IVP) for the system of crystal optics with polynomial data and a polynomial inhomogeneous term is suggested. The found solution of the IVP is a polynomial. Theoretical and computational analysis of polynomial solutions and their comparison with non-polynomial solutions corresponding to smooth data are given. The applicability of polynomial solutions to physical processes is discussed. An implementation of this method has been made by symbolic computations in Maple 10.

引用

页码：1469 / 1484

页数：16

共 50 条

[31] MULTISTEP METHOD OF THE NUMERICAL SOLUTION OF THE PROBLEM OF MODELING THE CIRCULATION OF ATMOSPHERE IN THE CAUCHY PROBLEM
Prusov, V. A.
Doroshenko, A. Yu.
CYBERNETICS AND SYSTEMS ANALYSIS, 2015, 51 (04) : 547 - 555
[32] NUMERICAL SOLUTION METHOD FOR THE CAUCHY PROBLEM FOR ELLIPTIC EQUATIONS.
Vabishchevich, P.N.
Pulatov, P.A.
Moscow University computational mathematics and cybernetics, 1984, (02) : 1 - 8
[33] Polynomial Decay of Solutions to the Cauchy Problem for a Petrovsky-Petrovsky System in Rn
Beniani, Abderrahmane
Benaissa, Abbes
Zennir, Khaled
ACTA APPLICANDAE MATHEMATICAE, 2016, 146 (01) : 67 - 79
[34] Regularization of a solution to the Cauchy problem for the system of equations of elasticity in displacements
Makhmudov, OI
Niezov, IE
SIBERIAN MATHEMATICAL JOURNAL, 1998, 39 (02) : 323 - 330
[35] REPRESENTATION OF A SOLUTION OF THE CAUCHY PROBLEM FOR AN OSCILLATING SYSTEM WITH PURE DELAY
Khusainov, D. Ya.
Diblik, J.
Ruzickova, M.
Lukacova, J.
NONLINEAR OSCILLATIONS, 2008, 11 (02): : 276 - 285
[36] Asymptotic solution of the cauchy problem for a singularly perturbed linear system
Kocherga O.I.
Ukrainian Mathematical Journal, 1999, 51 (8) : 1271 - 1274
[37] Regularization of a solution to the cauchy problem for the system of equations of elasticity in displacements
O. I. Makhmudov
I. È. Niezov
Siberian Mathematical Journal, 1998, 39 : 323 - 330
[38] A NEW SOLUTION OF CAUCHY PROBLEM FOR THE WAVE EQUATION AND THE EQUATION OF POISSON
WEINSTEIN, A
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1952, 58 (06) : 650 - 651
[39] DECOMPOSITION OF THE SOLUTION OF A HOMOGENEOUS CAUCHY-PROBLEM NEAR THE BOUNDARY OF A DOMAIN OF HOLOMORPHY FOR THE CAUCHY DATA
SCHILTZ, D
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1988, 306 (04): : 177 - 180
[40] A NEW METHOD FOR COMPUTING A COLUMN REDUCED POLYNOMIAL MATRIX
BEELEN, TGJ
VANDENHURK, GJ
PRAAGMAN, C
SYSTEMS & CONTROL LETTERS, 1988, 10 (04) : 217 - 224

← 1 2 3 4 5 →