linear differential equation example problems

... order linear Differential equations,” in Mathematics and Its Applications, Reidel, Dordrecht, the Netherlands, 1987. 2 L J. Guo, J P. Sun, and Y H. Zhao, “Existence of positive solutions for nonlinear ... Al-Malki, “Nonlinear three-point third-order boundary value problems, ” Applied Mathematics and Computation, vol. 190, no. 2, pp. 1168–1177, 2007. 11 S. Li, “Positive solutions of nonlinear singular ... max t∈I   T n u  t  ≤ M n t n n!  u  c , 3.39 10 Boundary Value Problems 13 Z. Du, W. Ge, and X. Lin, “Existence of solutions for a class of third-order nonlinear boundary value problems, ” Journal of Mathematical Analysis...

Ngày tải lên: 21/06/2014, 05:20

Ngày tải lên: 23/06/2014, 00:20

... . . . . . . . . . . . . . . . . . 1-40 2 Examples Examples of Elliptic Problems . . . . . . . . . . . . . . . . . . . . . . . . . 2-2 Poisson’s Equation on Unit Disk . . . . . . . . . . . ... •Time-dependent problems are easy to implement in the FEM context. The solution u(x,t) of the equation can be approximated by . This yields a system of ordinary differential equations (ODE) ... u, the PDE is called nonlinear and FEM yields a nonlinear system K(U) U= F(U). You can use iterative methods for solving the nonlinear system. The toolbox provides a nonlinear solver called...

Ngày tải lên: 26/01/2014, 02:20

... Solution • MethodofConvolution References 2.1 Differential Equations Afunctioncontainingvariablesandtheirderivativesiscalledadifferentialex pression,andanequation involvingdifferentialexpressionsiscalledadifferentialequation. Adifferentialequationisanordinary differential ... LLC 2 Ordinary Linear Differential and Difference Equations B.P. Lathi California State University, Sacramento 2.1 Differential Equations Classical Solution • MethodofConvolution 2.2 Difference Equations Initial ... discussion of differential equations can be found in numerous texts on the subject [1]. 2.2 Difference Equations Thedevelopmentofdifferenceequationsisparalleltothatofdifferentialequations. Weconsiderhere only...

Ngày tải lên: 27/01/2014, 03:20

Ngày tải lên: 14/03/2014, 13:20

... of linear differential equations (which we shall refer to simply as differential Galois theory) is the analogue for linear differential equations of the classical Galois theory for polynomial equations. ... zero. A linear differential equation is an equation of the form ∂Y = AY where A is an n × n matrix with entries in k although sometimes we shall also consider scalar linear differential equations ... order two equations gives an indication how this classification could be used for linear differential equations in characteristic 0. A more or less obvious observation is that these linear differential equations...

Ngày tải lên: 31/03/2014, 15:56

... constants. Equation 1.3 is termed a first-order, linear, ordinary differential equation with variable coefficients. These terms are explained below. Term Explanation Differential equation Equation ... exp(x) = e x . Equation 1.5 is easily verified as the solution to Equations 1.3 and 1.4 by substitution in these equations: Terms in Substitution of Equation 1.5 Equations 1.3 and 1.4 in Equations ... of a single ODE, Equation 1.3, subject to initial condition Equation 1.4, by the Euler and modified Euler methods, Equation 1.28 and Equations 1.30. The analytical solution, Equation 1.5, can be...

Ngày tải lên: 08/04/2014, 10:27

... positive solutions of singular nonlocal boundary value problems for systems of nonlinear second-order ordinary differential equations. Nonlinear Anal. 70, 444–451 (2009). doi:10.1016/j.na.2007.12.014 4. ... the following nonlocal equation with zero Dirichlet boundary condition −a ⎛ ⎝ 1  0 |u(s)| q ⎞ ⎠ u  (t )=h(t)f (u(t)) , when the nonlinearity f is a sublinear or superlinear function in a sense ... R 2 = || u || . Wang et al. Boundary Value Problems 2011, 2011:5 http://www.boundaryvalueproblems.com/content/2011/1/5 Page 7 of 11 Then, Equation 12 holds. Therefore, by Equations 10 and 12 and the first...

Ngày tải lên: 21/06/2014, 02:20

... Nieto, “Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions,” Boundary Value Problems, vol. 2009, Article ID 708576, ... Advances in Difference Equations 14 D. Jiang and C. Yuan, “The positive properties of the Green function for Dirichlet-type boundary value problems of nonlinear fractional differential equations and ... Nonlinear Analysis. Theory, Methods & Applications, vol. 72, no. 2, pp. 710–719, 2010. 15 S. Zhang, “Positive solutions for boundary-value problems of nonlinear fractional differential equations,”...

Ngày tải lên: 21/06/2014, 05:20

... Value Problems Volume 2011, Article ID 297026, 12 pages doi:10.1155/2011/297026 Research Article Positive Solution of Singular Boundary Value Problem for a Nonlinear Fractional Differential Equation Changyou ... 2006. 7 S. Zhang, “Positive solutions for boundary-value problems of nonlinear fractional differential equations,” Electronic Journal of Differential Equations , vol. 36, pp. 1–12, 2006. 8 Z. B. Bai ... boundary value problems, ” Boundary Value Problems, vol. 2009, Article ID 421310, 10 pages, 2009. 11 B. Ahmad and J. J. Nieto, “Existence results for nonlinear boundary value problems of fractional integrodifferential...

Ngày tải lên: 21/06/2014, 07:20

... the solution of the nonlinear Volterra integro-differential equation, which generalizes that developed in 1.Let us consider the nonlinear Volterra integro-differential equation y   t   f  t, ... 1 2 . 4. Numerical Examples The behaviour of the numerical method introduced above will be illustrated with the following two examples. Example 4.1. 22, Problem 2. The equation y   t   ... pages doi:10.1155/2010/470149 Research Article Biorthogonal Systems Approximating the Solution of the Nonlinear Volterra Integro -Differential Equation M. I. Berenguer, A. I. Garralda-Guillem, and M. Ruiz Gal ´ an Departamento...

Ngày tải lên: 21/06/2014, 10:20

... stability in the metric C 1 . 4. Examples In this part we consider two examples. Auxiliary numerical computations were performed by using MATLAB & SIMULINK R2009a. Example 4.1. We will investigate ... Corporation Boundary Value Problems Volume 2010, Article ID 956121, 20 pages doi:10.1155/2010/956121 Research Article Exponential Stability and Estimation of Solutions of Linear Differential Systems ... Illustrative examples are shown and comparisons with known results are given. 1. Introduction This paper will provide estimates of solutions of linear systems of neutral differential equations with...

Ngày tải lên: 21/06/2014, 11:20

... bt a, b > 0, the equation involved in problem P λ  is the stationary analogue of the well-known equation proposed by Kirchhoff in 1.Thisisoneofthe motivations why problems like P λ  ... papers, the nonlinearity f is again satisfying suitable growth conditions at 0 and ∞. Finally, in 6, where the nonlinearity t s−1  is replaced by a more general hx, t and the nonlinearity f ... for a quasilinear elliptic equation of Kirchhoff type,” Computers & Mathematics with Applications, vol. 49, no. 1, pp. 85–93, 2005. 4 A. Bensedik and M. Bouchekif, “On an elliptic equation...

Ngày tải lên: 21/06/2014, 11:20

... of boundary value problems with integral boundary conditions arise naturally in thermal conduction problems 15, semiconductor problems 16, hydrodynamic problems 17. Such problems include ... Corporation Boundary Value Problems Volume 2011, Article ID 456426, 19 pages doi:10.1155/2011/456426 Research Article Positive Solutions of nth-Order Nonlinear Impulsive Differential Equation with Nonlocal Boundary ... Nieto, “Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions,” Boundary Value Problems, vol. 2009, Article ID 708576,...

Ngày tải lên: 21/06/2014, 16:20

Ngày tải lên: 21/06/2014, 16:20

Ngày tải lên: 21/06/2014, 17:20

Ngày tải lên: 22/06/2014, 03:20

Ngày tải lên: 22/06/2014, 11:20

Ngày tải lên: 22/06/2014, 18:20

Ngày tải lên: 22/06/2014, 21:20