zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Laguerre polynomial approach for solving linear delay difference equations. (English) Zbl 1211.65166
Summary: We present a numerical method for the approximate solution of mth-order linear delay difference equations with variable coefficients under the mixed conditions in terms of Laguerre polynomials. The aim of this article is to present an efficient numerical procedure for solving mth-order linear delay difference equations with variable coefficients. Our method depends mainly on a Laguerre series expansion approach. This method transforms linear delay difference equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equation. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computer algebraic system Maple.
65Q10Numerical methods for difference equations
39A12Discrete version of topics in analysis
[1]Ajello, W. G.; Freedman, H. I.; Wu, J.: A model of stage structured population growth with density depended time delay, SIAM J. Appl. math. 52, 855-869 (1992)
[2]Hwang, C.: Solution of a functional differential equation via delayed unit step functions, Int. J. Syst. sci. 14, No. 9, 1065-1073 (1983) · Zbl 0509.93026 · doi:10.1080/00207728308926514
[3]Hwang, C.; Shih, Y. -P.: Laguerre series solution of a functional differential equation, Int. J. Syst. sci. 13, No. 7, 783-788 (1982) · Zbl 0483.93056 · doi:10.1080/00207728208926388
[4]El-Safty, A.; Abo-Hasha, S. M.: On the application of spline functions to initial value problems with retarded argument, Int. J. Comput. math. 32, 173-179 (1990) · Zbl 0752.65057 · doi:10.1080/00207169008803825
[5]Arikoglu, A.; Özkol, I.: Solution of difference equations by using differential transform method, Appl. math. Comput. 174, 1216-1228 (2006) · Zbl 1138.65309 · doi:10.1016/j.amc.2005.06.013
[6]Derfel, G.: On compactly supported solutions of a class of functional – differential equations, , 255 (1980)
[7]El-Safty, A.; Salim, M. S.; El-Khatib, M. A.: Convergence of the spline function for delay dynamic system, Int. J. Comput. math. 80, No. 4, 509-518 (2003) · Zbl 1022.65075 · doi:10.1080/0020716021000014204
[8]Karakoç, F.; Bereketo&gbreve, H.; Lu: Solutions of delay differential equations by using differential transform method, Int. J. Comput. math. 86, 914-923 (2009)
[9]Parand, K.; Razzaghi, M.: Rational Chebyshev tau method for solving higher-order ordinary differential equations, Int. J. Comput. math. 81, 73-80 (2004) · Zbl 1047.65052 · doi:10.1080/00207160310001606061a
[10]Tang, X. H.; Yu, J. S.; Peng, D. H.: Oscillation and nonoscillation of neutral difference equations with positive and negative coefficients, Comput. math. Appl. 39, 169-181 (2000) · Zbl 0958.39016 · doi:10.1016/S0898-1221(00)00073-0
[11]Xiong, W.; Liang, J.: Novel stability criteria for neutral systems with multiple time delays, Chaos solitons fract. 32, 1735-1741 (2007) · Zbl 1146.34330 · doi:10.1016/j.chaos.2005.12.020
[12]Zhou, J.; Chen, T.; Xiang, L.: Robust synchronization of delayed neural networks based on adaptive control and parameters identification, Chaos solitons fract. 27, 905-913 (2006) · Zbl 1091.93032 · doi:10.1016/j.chaos.2005.04.022
[13]Zhang, Q.; Wei, X.; Xu, J.: Stability analysis for cellular neural networks with variable delays, Chaos solitons fract. 28, 331-336 (2006) · Zbl 1084.34068 · doi:10.1016/j.chaos.2005.05.026
[14]Ocalan, O.; Duman, O.: Oscillation analysis of neutral difference equations with delays, Chaos solitons fract. 39, No. 1, 261-270 (2009) · Zbl 1197.39004 · doi:10.1016/j.chaos.2007.01.094
[15]Zhu, Wei: Invariant and attracting sets of impulsive delay difference equations with continuous variables, Comput. math. Appl. 55, No. 12, 2732-2739 (2008) · Zbl 1142.39312 · doi:10.1016/j.camwa.2007.10.020
[16]Sezer, M.: A method for approximate solution of the second order linear differential equations in terms of Taylor polynomials, Int. J. Math. educ. Sci. technol. 27, No. 6, 821-834 (1996) · Zbl 0887.65084 · doi:10.1080/0020739960270606
[17]Gulsu, M.; Sezer, M.: A method for the approximate solution of the high-order linear difference equations in terms of Taylor polynomials, Int. J. Comput. math. 82, No. 5, 629-642 (2005) · Zbl 1072.65164 · doi:10.1080/00207160512331331156
[18]Gulsu, M.; Sezer, M.: Polynomial solution of the most general linear Fredholm integrodifferential-difference equations by means of Taylor matrix method, Complex variables 50, No. 5, 367-382 (2005) · Zbl 1077.45006 · doi:10.1080/02781070500128354
[19]Gulsu, M.; Sezer, M.: A method for the approximate solution of the high-order linear difference equations in terms of Taylor polynomials, Int. J. Comput. math. 82, No. 5, 629-642 (2005) · Zbl 1072.65164 · doi:10.1080/00207160512331331156
[20]ş Nas, .; Yalçınbaş, S.; Sezer, M.: A Taylor polynomial approach for solving high-order linear Fredholm integro-differential equations, Int. J. Math. educ. Sci. technol. 31, No. 2, 213-225 (2000)
[21]Kanwal, R. P.; Liu, K. C.: A Taylor expansion approach for solving integral equation, Int. J. Math. educ. Sci. technol. 20, No. 3, 411-414 (1989) · Zbl 0683.45001 · doi:10.1080/0020739890200310
[22]Fox, L.; Mayers, D. F.; Ockendon, J. R.; Tayler, A. B.: On a functional differential equation, J. inst. Math. appl. 8, 271-307 (1971) · Zbl 0251.34045 · doi:10.1093/imamat/8.3.271
[23]Saaty, T. L.: Modern nonlinear equations, (1981)
[24]Kreyszig, E.: Introductory functional analysis with applications, (1978)