nonlinear differential equations examples

... higher-order nonlinear fractional differential equations. Fixed Point Theory Appl 2010, 2010:1-17. 30. Babakhani A: Positive solutions for system of nonlinear fractional differential equations in ... problems of nonlinear fractional differential equations. Commun Nonlinear Sci Numer Simul 2011, 16:2086-2097. 20. Yu Y, Jiang D: Multiple Positive Solutions for the Boundary Value Problem of A Nonlinear ... nonlinear fractional differential equations. Int J Differ Equ 2010, 2010:1-12. 28. Ahmad B, Nieto JJ: Existence results for a coupled system of nonlinear fractional differential equations with three- point...

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... neutral functional differential equations. Arch Ration Mech Anal. 19, 149–166 (1965). doi:10.1007/BF00282279 doi:10.1186/1029-242X-2011-20 Cite this article as: Zheng and Feng: Some new nonlinear integral ... 2011:20 http://www.journalofinequalitiesandapplications.com/content/2011/1/20 Page 14 of 15 RESEARC H Open Access Some new nonlinear integral inequalities and their applications in the qualitative analysis of differential equations Bin Zheng 1* and Qinghua Feng 1,2 * ... paper, some new nonlinear integral inequalities are established, which provide a handy tool for analyzing the global existence and boundedness of solutions of differential and integral equations. ...

Ngày tải lên: 21/06/2014, 01:20

... conditions for differ- ential equations or impulsive differential equations. To the best of our knowledge it is the first article to deal with integro -differential equations with “an ti-peri odic” ... of solutions for first-order nonlinear integro -differential equations with boundary value conditions. Our methods to prove the existence of solutions involve new differential inequalities and ... 34D09,34D99. Keywords: Boundary value problems, integro -differential equations, fixed-point motheds 1. Introduction and preliminaries As is known, integro -differential equations find many applications in various...

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... America). Chapter 19. Partial Differential Equations 19.0 Introduction The numerical treatment of partial differential equations is, by itself, a vast subject. Partial differential equations are at the ... Recipes dealing with partial differential equations alone. (The references [1-4] provide, of course, available alternatives.) In most mathematics books, partial differential equations (PDEs) are classified into ... possible choices for ellipticsecond-order equations, but morecomplicated boundaryconditions can also be encountered.) 834 Chapter 19. Partial Differential Equations Sample page from NUMERICAL RECIPES...

Ngày tải lên: 28/10/2013, 22:15

... error is one associated with nonlinear hyperbolic equations and is therefore sometimes called nonlinearinstability. For example, a piece of the Euler or Navier-Stokes equations for fluid flow looks ... s n−1/2 and r n being needed to advance the solution. For equations more complicated than our simple model equation, especially nonlinear equations, the leapfrog method usually becomes unstable ... schemes, which require us to solve implicit equations coupling the u n+1 j for various j. (Explicit and implicit methods for ordinary differential equations were discussed in Đ16.6.) The FTCS...

Ngày tải lên: 07/11/2013, 19:15

... of Ordinary Differential Equations 16.0 Introduction Problems involving ordinary differential equations (ODEs) can always be reduced to the study of sets of first-order differential equations. ... by the differential equations. Boundary conditionscan be as simple as requiring that certain variables have certain numerical values, or as complicated as a set of nonlinear algebraic equations ... auxiliary variables. The generic problem in ordinary differential equations is thus reduced to the study of a set of N coupled first-order differential equations for the functions y i ,i=1,2, ,N, having...

Ngày tải lên: 15/12/2013, 04:15

... 1973, Computational Methods in Ordinary Differential Equations (New York: Wiley). Lapidus, L., and Seinfeld, J. 1971, Numerical Solution of Ordinary Differential Equations (New York: Academic Press). 16.1 ... REFERENCES AND FURTHER READING: Gear, C.W. 1971, Numerical Initial Value Problems in Ordinary Differential Equations (Englewood Cliffs, NJ: Prentice-Hall). Acton, F.S. 1970, Numerical Methods That ... 710 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN...

Ngày tải lên: 15/12/2013, 04:15

... 848 Chapter 19. Partial Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... not as easy. The replacement (19.2.22) with n → n +1leaves us with a nasty set of coupled nonlinear equations to solve at each timestep. Often there is an easier way: If the form of D(u) allows ... given the initial wavepacket, ψ(x, t =0), together with boundary 852 Chapter 19. Partial Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN...

Ngày tải lên: 15/12/2013, 04:15

... 856 Chapter 19. Partial Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... U 2 (u n+(1/m) , ∆t) ··· u n+1 = U m (u n+(m−1)/m , ∆t) (19.3.20) 854 Chapter 19. Partial Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... again! CITED REFERENCES AND FURTHER READING: Ames, W.F. 1977, Numerical Methods for Partial Differential Equations , 2nd ed. (New York: Academic Press), Chapter 2. Goldberg, A., Schey, H.M., and...

Ngày tải lên: 15/12/2013, 04:15