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

[1] Symbolic Computation of an Exact Solution of the Cauchy Problem for the System of Crystal Optics with Polynomial Data
Yakhno, Valery
Altunkaynak, Meltem
NUMERICAL ANALYSIS AND ITS APPLICATIONS: 4TH INTERNATIONAL CONFERENCE, NAA 2008, 2009, 5434 : 596 - +
[2] Cauchy problem for the system of crystal optics equations
Zhura, N. A.
DOKLADY MATHEMATICS, 2007, 75 (01) : 118 - 122
[3] Cauchy problem for the system of crystal optics equations
N. A. Zhura
Doklady Mathematics, 2007, 75 : 118 - 122
[4] NEW METHOD FOR SOLUTION OF CAUCHY-PROBLEM FOR PARABOLIC EQUATIONS
MOORE, J
ROBINSON, P
COMMUNICATIONS OF THE ACM, 1972, 15 (12) : 1050 - &
[5] A Method for Solution of the Cauchy Problem with Polynomial Coefficients and Some Applications to Problems on Management of Investment Portfolios
Asekov A.Z.
Kovalenko E.V.
Journal of Mathematical Sciences, 2016, 216 (5) : 674 - 678
[6] POINTWISE BOUNDS FOR SOLUTION OF A CAUCHY PROBLEM IN TERMS OF CAUCHY DATA
SATHER, D
JOURNAL OF DIFFERENTIAL EQUATIONS, 1967, 3 (02) : 286 - &
[7] SOLUTION OF CAUCHY PROBLEM AND OF MIXED PROBLEM FOR A PARABOLIC SYSTEM
RASULOV, ML
DOKLADY AKADEMII NAUK SSSR, 1968, 180 (06): : 1300 - &
[8] An interpolating polynomial method for liquid crystal display optics
Barrick, GF
JAPANESE JOURNAL OF APPLIED PHYSICS PART 1-REGULAR PAPERS SHORT NOTES & REVIEW PAPERS, 2002, 41 (08): : 5480 - 5485
[9] An interpolating polynomial method for liquid crystal display optics
Barrick, George F.
Japanese Journal of Applied Physics, Part 1: Regular Papers and Short Notes and Review Papers, 2002, 41 (08): : 5480 - 5485
[10] Regularization of a solution to the Cauchy problem for the system of thermoelasticity
Makhmudov, OI
Niyozov, IE
Complex Analysis and Dynamical Systems II, 2005, 382 : 285 - 289

← 1 2 3 4 5 →