non homogeneous linear partial differential equation with constant coefficients

... pdeeig. ãIf the coefficients c, a, f, q, or g are functions of 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 ... . . 4-28 Fast Solution of Poisson’s Equation . . . . . . . . . . . . . . . . . . . . 4-29 Partial Differential Equation Toolbox For Use with MATLABđ Users Guide Computer ... eigenvalue problem is a homogeneous problem, i.e., g = 0, r = 0.) In the nonlinear case, the coefficients, g, q, h, and r can depend on u, and for the hyperbolic and parabolic PDE, the coefficients can...

Ngày tải lên: 26/01/2014, 02:20

... note deals with two fully parallel methods for solving linear partial differential- algebraic equations (PDAEs) of the form: Au t + B∆u = f(x, t) (1) where A is a singular, symmetric and nonnegative ... high-performance computers are also reported. Keywords: Differential- algebraic equation (DAE), partial differential- algebraic equation (PDAE), nonnegative pencil of matrices, parallel method 1. Introduction Recently ... Section 2 deals with some properties of the so called nonnegative pencils of matrices. In Section 3 we describe two parallel methods for solving linear PDAEs, whose coefficients found a nonnegative...

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Ngày tải lên: 22/03/2014, 11:20

... positive 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 ... Methods We start with the numerical solution 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....

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Ngày tải lên: 12/06/2014, 16:17

... Differential Equations, no. 36, pp. 1–12, 2006. 16 M. Benchohra, S. Hamani, and S. K. Ntouyas, “Boundary value problems for differential equations with fractional order and nonlocal conditions,” Nonlinear ... Difference Equations Volume 2011, Article ID 546038, 14 pages doi:10.1155/2011/546038 Research Article The Existence of Positive Solution to a Nonlinear Fractional Differential Equation with Integral ... for nonlinear fractional differential equations,” Computers & Mathematics with Applications, vol. 59, no. 3, pp. 1363–1375, 2010. 21 S. Zhang, “The existence of a positive solution for a nonlinear...

Ngày tải lên: 21/06/2014, 05:20

... pages doi:10.1155/2011/456426 Research Article Positive Solutions of nth-Order Nonlinear Impulsive Differential Equation with Nonlocal Boundary Conditions Meiqiang Feng, 1 Xuemei Zhang, 2 and Xiaozhong ... a nonlinear nth order boundary value problem with nonlocal conditions,” Applied Mathematics Letters, vol. 18, no. 5, pp. 521–527, 2005. 20 R. Ma and H. Wang, “Positive solutions of nonlinear ... devoted to study a class of nonlocal BVPs for nth-order impulsive differential equations with fixed moments. Consider the following nth-order impulsive differential equations with integral boundary conditions: x n  t  ...

Ngày tải lên: 21/06/2014, 16:20

... differential equations with fractional order and nonlocal conditions,” Nonlinear Analysis: Theory, Methods and Applications, vol. 71, no. 7-8, pp. 2391–2396, 2009. 17 H. A. H. Salem, “On the nonlinear ... differential equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 69, no. 8, pp. 2677–2682, 2008. 8 V. Lakshmikantham, “Theory of f ractional functional differential equations,” Nonlinear ... problems of nonlinear fractional differential equations,” Electronic Journal of Differential Equations, vol. 2006, pp. 1–12, 2006. 21 S. Zhang, “The existence of a positive solution for a nonlinear...

Ngày tải lên: 21/06/2014, 16:20

... articles dealing with the existence of solutions to boundary value problems for fractional differential equation with p-Laplacian operator. In [24], the authors investigated the nonlinear nonlocal problem        D β 0+ (φ p (D α 0+ u))(t) ... boundary value problem of nonlinear fractional differ- ential equation. J. Math. Anal. Appl. 311, 495–505 (2005) [35] Leggett, RW, Williams, LR: Multiple positive solutions of nonlinear operators on ... 0 (such as BVP (1.1)) with b = 0. It is a well-known fact that the boundary value problems with Sturm–Liouville boundary value conditions for integral order differential equations have important...

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Ngày tải lên: 08/04/2015, 15:29

... comparisons with known results are given. 1. Introduction This paper will provide estimates of solutions of linear systems of neutral differential equations with constant coefficients and a constant ... pages doi:10.1155/2010/956121 Research Article Exponential Stability and Estimation of Solutions of Linear Differential Systems of Neutral Type with Constant Coefficients J. Ba ˇ stinec, 1 J. Dibl ´ ık, 1, 2 D. Ya. Khusainov, 3 and ... c 2  t t−h 2  ˙x  s   ds 1.7 is used with suitable constants c 1 and c 2 .In7, 8, functionals depending on derivatives are also suggested for investigating the asymptotic stability of neutral nonlinear systems. The...

Ngày tải lên: 21/06/2014, 11:20

... solutions to linear differential equations and systems of equations exemplify important ideas in linear algebra, and how linear algebra often answers key questions regarding differential equations. ã ... general solutions to systems of linear differential equations or higher order linear differential equations. Over the past decade or two, first-order differential equations have become a standard ... Matrix exponential 270 4 Higher order differential equations 273 4.1 Motivating equations 273 4.2 Homogeneous equations: distinct real roots 274 4.3 Homogeneous equations: repeated and complex roots...

Ngày tải lên: 11/06/2014, 07:16

... Poland Abstract The article deals with functional differential inequalities generated by the Cauchy problem for nonlinear first-order partial functional differential equations. The unknown function ... Iterative Techniques for Nonlinear Differential Equations. Pitmann Advanced Publishing Program, Boston (1985) 4. Lakshimkantham, V, Vatsala, AS: Generalized Quasilinearization for Nonlinear Problems. ... partial differential functional equations. Nonlinear Anal TMA. 14, 837–850 (1990). doi:10.1016/0362-546X(90)90024-B 14. Topolski, K: On the uniqueness of viscosity solutions for first order partial...

Ngày tải lên: 21/06/2014, 02:20

... model at hand. Indeed, we are dealing with a dynamical system with piecewise constant nonlinear- lities see e.g., 2–6, and the usual linear and continuity arguments cannot be applied to our 1.3. ... difference equations with periodic coefficients and nonlinear control functions,” Discrete Dynamics in Nature and Society, vol. 2008, Article ID 179589, 21 pages, 2008. Advances in Difference Equations ... Difference Equations Volume 2010, Article ID 542073, 13 pages doi:10.1155/2010/542073 Research Article Complete Asymptotic and Bifurcation Analysis for a Difference Equation with Piecewise Constant...

Ngày tải lên: 21/06/2014, 11:20

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