ELEMENTARY DIFFERENTIAL EQUATIONS BOYCE

[in Russian], Nauka Publishers, Moscow, 1974.Boyce, W. E. and DiPrima, R. C., Elementary Differential Equations and Boundary Value Problems, 8thEdition, John Wiley & Sons, New York, 2004.Braun, M., Differential Equations and Their Applications, 4th E[r]

NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS NUMERICAL SOLUTIONS OF OR[r]

RESEARC H Open AccessSingular integrals of the compositions of Laplace-Beltrami and Green’s operatorsRu Fang1*and Shusen Ding2* Correspondence: fangr@hit.edu.cn1Department of Mathematics,Harbin Institute of TechnologyHarbin 150001, P.R.ChinaFull list of author information isavailable at the end of t[r]

functional differential equations w ith a non-dense domain,” Acta Mathematica Sinica (EnglishSeries), vol. 20, no. 5, pp. 933–942, 2004.[19] M. Laklach, “Contribution`al’´etude des´equations aux d´eriv´ees part ielles`aretardetdetypeneutre,” Th`ese de doctorat, l’Universit´e de Pau et d[r]

Evolution Equations, North-Holland, Amsterdam, 1982.Cariello, F. and Tabor, M., Painlev´e expansions for nonintegrable evolution equations, Physica D, Vol. 39,No. 1, pp. 77–94, 1989.Clarkson, P. A. and Kruskal, M. D., New similarity reductions of the Boussinesq equation, J. Math. Phys.[r]

ematiques, Universit´e de Boumerd`es, Avenue de l’Ind´ependance,35000 Boumerd`es, AlgeriaCorrespondence should be addressed to Mouffak Benchohra, benchohra@univ-sba.dzReceived 30 January 2009; Revised 23 March 2009; Accepted 15 May 2009Recommended by Juan J. NietoThe aim of this paper is to investiga[r]

Liapunov’s direct method has been successfully used to investigate stability properties of awide variety of differential equations. However, there are many difficulties encountered inthe study of stability by means of Liapunov’s direct method. Recently, Burton 1–4,Jung5,Luo 6,andZhang7 s[r]

ao Preto, SP, Brazil3Departamento de Matem´atica y Estad´ıstica, Universidad de La Frontera, Casilla 54-D, Temuco, ChileCorrespondence should be addressed to Claudio Cuevas, cch@dmat.ufpe.brReceived 23 September 2010; Accepted 8 December 2010Academic Editor: J. J. TrujilloCopyright q 2011 Claudio C[r]

the NSF of China (no. 10671046).References[1] M.Biroli,“Surlessolutionsborn´ees ou presque p´eriodiques des´equations d’´evolution multivo-quessurunespacedeHilbert,”Ricerche di Matematica, vol. 21, pp. 17–47, 1972.[2] C. M. Dafermos, “Almost periodic processes and almost periodic solutions of[r]

.Fractional differential equations have proved to be an excellent tool in the mathematicmodeling of many systems and processes in various fields of science and engineering.Indeed, we can find numerous applications in viscoelasticity, electrochemistry, control,2 Advances in Difference Equationsele[r]

Hindawi Publishing CorporationAdvances in Difference EquationsVolume 2011, Article ID 404917, 16 pagesdoi:10.1155/2011/404917Research ArticleNonlocal Boundary Value Problem for ImpulsiveDifferential Equations of Fractional OrderLiu Yang1, 2and Haibo Chen11Department of Mathematics, Central Sou[r]

EURASIP Journal on Applied Signal Processing 2004:12, 1770–1777c 2004 Hindawi Publishing CorporationNonlinear Transformation of DifferentialEquations into Phase SpaceLeon CohenDepartment of Physics and Astronomy, Hunter College, City University of New York, 695 Park Avenue, New York, NY 10021, USAE[r]

6.2.3. Theorems about Differentiable Functions. L’Hospital Rule . . . . . . . . . . . . . . . . . 2546.2.4. Higher-Order Derivatives and Differentials. Taylor’s Formula . . . . . . . . . . . . . . . 2556.2.5. Extremal Points. Points of Inflection 2576.2.6. Qualitative Analysis of Functions and Constr[r]

− αun+1j+1= unj,j=1,2...J − 1(19.2.9)whereα ≡D∆t(∆x)2(19.2.10)19.2 Diffusive Initial Value Problems849Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright (C) 1988-1992 by Cambridge University Press.Programs Copyright (C) 1988-1992 by Numerical Reci[r]

(n)+q0t(n−1)/4x(√t)=0, n ≥ 3, t ≥ 1.(3:9)It is easy to verify that all conditions of Corollary 3.5 are satisfied. Hence, every solu-tion of (3.9) is oscillatory or tends to zero as t ® ∞.Example 3.12. Consider the even-order neutral differential equation (2.15).Applying Corollary 3.8, we kno[r]

integrodifferential boundary value problems with p-Laplacian,” Boundary Value Problems, vol. 2007,Article ID 57481, 9 pages, 2007.7 D. R. Anderson, “Solutions to second-order three-point problems on time scales,” Journal of DifferenceEquations and Applications, vol. 8, no. 8, pp. 673–688, 2002.8 D[r]

Galbraith, I., Ching, Y.S., and Abraham, E. 1984,American Journal of Physics, vol. 52, pp. 60–68. [2]19.3 Initial Value Problems in MultidimensionsThe methods described in §19.1 and §19.2 for problems in 1+1dimension(one space and one time dimension) can easily be generalized to N +1dimensions.Howev[r]

Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copying of machine-readable files (including this one) to any servercomputer, is strictly prohibited. To order Numerical Recipes books,diskettes, or CDROMsvisit website http://w[r]

Press, Boca Raton, 1994–1996.Jimbo, M., Kruskal, M. D., and Miwa, T., Painlev´e test for the self-dual Yang–Mills equation, Phys. Lett.,Ser. A, Vol. 92, No. 2, pp. 59–60, 1982.Kudryashov, N. A., Analytical Theory of Nonlinear Differential Equations [in Russian], Institut kompjuternyhis[r]

√axt– 3at2+ B(x +√at)+ψ2(η), η = x – t√a.Remark. In the special case of a = 1, b < 0,andc > 0, equation (15.7.2.22) describes spatial transonicflows of an ideal polytropic gas.15.8. Classical Method of Studying Symmetries ofDifferential EquationsPreliminary remarks. The classical metho[r]