numerical solution second order differential equation matlab

Ngày tải lên: 13/08/2014, 16:20

... Y Δ achieves an order γ of strong convergence, then it also achieves at least an order β = γ of weak convergence. We emphasize that the weak order obtained above is usually not sharp and, thus, the order ... only require numerical recipes. Together with Nicola Bruti-Liberati we had for several years planned a book to follow on the book with Peter Kloeden on the Numerical Solution of Stochastic Differential Equations”, ... weighted index ODE ordinary differential equation SDE stochastic differential equation PDE partial differential equation PIDE partial integro differential equation I ν (·) modified Bessel function...

Ngày tải lên: 19/02/2014, 22:20

... methods when we solve super- linear differential equations such as elliptic problems, Dirac equations, Hamiltonian systems, wave equations, and Schrödinger equations. Theorem 3.2. Assume that ... (1986) doi:10.1186/1687-2770-2011-33 Cite this article as: Zhang et al.: Infinitely many periodic solutions for some second- order differential systems with p(t)-Laplacian. Boundary Value Problems 2011 2011:33. Submit ... 2011:33 http://www.boundaryvalueproblems.com/content/2011/1/33 Page 10 of 15 RESEARC H Open Access Infinitely many periodic solutions for some second- order differential systems with p(t)- Laplacian Liang Zhang, Xian Hua Tang * and Jing...

Ngày tải lên: 20/06/2014, 22:20

... distribution and trace formula of a second order operator- differential equation Nigar Mahar Aslanova 1,2 Correspondence: nigar. aslanova@yahoo.com 1 Department of Differential Equation, Institute of Mathematics and ... problems for differential- operator equations. Nauk Dumka, Kiev, 284 (1984) (Russian). 31. Yakubov, S, Yakubov, Ya: Differential- Operator Equations Ordinary and Partial Differential Equations. Chapman ... simple identity for eigenvalue of second order differential operator. DAN SSSR. 88(4), 593–596 (1953) 19. Aslanova, NM: Trace formula for Sturm-Liouville operator equation. Proc Math Mech Natl Acad...

Ngày tải lên: 21/06/2014, 02:20

... boundary value problem of third -order differential equations,” Mathematica Slovaca, vol. 60, no. 4, pp. 485–494, 2010. 4 Y. Sun, “Positive solutions for third -order three-point nonhomogeneous ... “Third 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 ... 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 third -order two-point...

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Ngày tải lên: 11/10/2014, 04:02

Ngày tải lên: 11/10/2014, 04:03

... Difference Equations Volume 2009, Article ID 143175, 14 pages doi:10.1155/2009/143175 Research Article On the Spectrum of Almost Periodic Solution of Second- Order Neutral Delay Differential Equations with ... contradiction. The claim follows. 14 Advances in Difference Equations 12 R. Yuan, “On the spectrum of almost periodic solution of second- order differential equations with piecewise constant argument,” Nonlinear ... periodic differential equations and almost periodic flows,” Journal of Differential Equations, vol. 5, no. 1, pp. 167–181, 1969. 18 R. Yuan, “Pseudo-almost periodic solutions of second- order neutral...

Ngày tải lên: 21/06/2014, 20:20

... and modified Euler methods, Equation 1.28 and Equations 1.30. The analytical solution, Equation 1.5, can be used to calculate the exact errors in the numerical solutions. Equation 1.3 models the ... 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...

Ngày tải lên: 08/04/2014, 10:27

... otherwise, the solution is said to be nontrivial. If the solution is a nontrivial solution, then we can further divide the solution into two cases: non-oscillatory solution and oscillatory solution. ... kind of second- order rational difference equation. With the change of the initial values, we find the successive lengths of positive and negative semicycles for oscillatory solutions of this equation, ... non-oscillatory solutions of Equation (1.1) with x - 1 , x 0 ẻ (0, 1), which must be eventually negative. There do not e xist eventua lly positive non-oscillatory solutions of Equation (1.1). Proof....

Ngày tải lên: 20/06/2014, 22:20

... in 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 ... preliminaries for discussing the existence of positive solutions of boundary value problem 1.5. Advances in Difference Equations 5 Therefore, the unique solution of BVP 2.1 is x  t   − 1 Γ  α   t 0  t ... 710–719, 2010. 15 S. Zhang, “Positive solutions for boundary-value problems of nonlinear fractional differential equations,” Electronic Journal of Differential Equations, no. 36, pp. 1–12, 2006. 16...

Ngày tải lên: 21/06/2014, 05:20

... of maximal and minimal solutions for 1.2. Definition 4.1. Let mt be a solution of 1.2 in 0, 1, then mt is said to be a maximal solution of 1.2, if for every solution ut of 1.2 ... problem for a second- order differential equation with fractional derivatives in the lower terms,” Differentsial’nye Uravneniya, vol. 18, no. 2, pp. 341–342, 1982. 6 S. Zhang, “Existence of solution ... IVPs,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 3, pp. 674–684, 2009. 24 Y. Chen and H L. An, Numerical solutions of coupled Burgers equations with time- and space- fractional...

Ngày tải lên: 21/06/2014, 07:20

... properly cited. This paper deals with obtaining a numerical method in order to approximate the solution of the nonlinear Volterra integro-differential equation. We define, following a fixed-point approach, a ... integro- differential equations with weakly singular kernels,” BIT, vol. 41, no. 5, pp. 891–900, 2001. 7 H. Brunner and P. J. van der Houwen, The Numerical Solution of Volterra Equations, vol. 3 ... Gal ´ an, and M. C. Serrano P ´ erez, “Analytical techniques for a numerical solution of the linear Volterra integral equation of the second kind,” Abstract and Applied Analysis, vol. 2009, Article...

Ngày tải lên: 21/06/2014, 10:20

... has the second solution at λ, μ. By the definition of O, there exists ε>0 such that λ, μ ∈O ε,1 ∪Γ ε . That is 4.1 has a positive solution at λ, μ. So let u ε ,v ε  be a positive solution ... pages doi:10.1155/2011/212980 Research Article Multiple Positive Solutions of a Singular Emden-Fowler Type Problem for Second- Order Impulsive Differential Systems Eun Kyoung Lee and Yong-Hoon Lee Department ... and multiplicity of positive solutions of a singular boundary value problem for second- order differential systems with impulse effects. By using the upper and lower solutions method and fixed point...

Ngày tải lên: 21/06/2014, 11:20

... nonnegative solutions for second order impulsive differential equations,” Applied Mathematics and Computation, vol. 114, no. 1, pp. 51–59, 2000. 9 B. Liu and J. Yu, “Existence of solution of ... Problems 11 E. Lee and Y. Lee, “Multiple positive solutions of singular two point boundary value problems for second order impulsive differential equations,” Applied Mathematics and Computation, ... 64–82, 2009. 14 M. Feng and D. Xie, “Multiple positive solutions of multi-point boundary value problem for second- order impulsive differential equations,” Journal of Computational and Applied Mathematics,...

Ngày tải lên: 21/06/2014, 16:20

... positive solutions of nth order m-point boundary value problem,” Applied Mathematics and Computation, vol. 182, no. 2, pp. 1231–1239, 2006. 27 J. Yang and Z. Wei, “Positive solutions of nth order ... differential equations,” Applied Mathematics Letters, vol. 21, no. 8, pp. 828–834, 2008. 10 B. Ahmad and J. J. Nieto, “Existence of solutions for nonlocal boundary value problems of higher- order ... and E. Mboumi, “Positive solutions of a boundary value problem for a nonlinear fractional differential equation, ” Electronic Journal of Qualitative Theory of Differential Equations, vol. 2008, no....

Ngày tải lên: 21/06/2014, 16:20