numerical solution second order differential equation matlab

... these phenomena The analysis starts with a second-order differential equation, free of constants, that offers a general way of describ-ing them This equation is then integrated and applied to ... first-order D.E for the slope,Integrating again and rearranging gives This algebraic relation, when substituted into equation (1), satisfies the second-order D.E Therefore, it is a general solution ... saturation curve, described in terms of its independent (x) and dependent (y) variables, a second-order differential equation is obtained that applies to any saturation phenomena It shows that the driving

Ngày tải lên: 13/08/2014, 16:20

... 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 F(t, ... In this article, we investigate the existence of infinitely many periodic solutions for some nonautonomous second-order differential systems with p(t)-Laplacian Some multiplicity results are obtained ... Classification: 34C37; 58E05; 70H05 Keywords: p(t)-Laplacian, Periodic solutions, Critical point theory 1 Introduction Consider the second-order differential system with p(t)-Laplacian ⎧ ⎨ ⎩ −d dt(|˙u(t)|p(t)−2˙u(t))

Ngày tải lên: 20/06/2014, 22:20

... beginning with some k, Equation 2.6 has exactly one positive root corresponding to the imaginary root of Equation 2.5 Now, find the asymptotic of the imaginary roots of Equation 2.5 For z = iy ... L0which are less than gk Now, find the asymptotic of those solutions of Equation 2.3 which are greater than gk, i.e., the real roots of Equation 2.5 By virtue of the asymptotic for a large |z| ... self-adjointness of that operator His approach was used by Fulton in [3] later on As for the differential operator equations, to the best of this author’s knowledge inthe articles [1,4-6], an eigenvalue

Ngày tải lên: 21/06/2014, 02:20

... 10 pagesdoi:10.1155/2011/483057 Research Article Iterative Solutions of Singular Boundary Value Problems of Third-Order Differential Equation Peiguo Zhang Department of Elementary Education, Heze ... singular 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 boundary ... have been many papers investigating the solutions of three-point BVPs, see 2 5, 10, 12 and references therein Recently, the existence of solutions of third-order three-point BVP1.1 has been studied

Ngày tải lên: 21/06/2014, 05:20

... 905769, 28 pagesdoi:10.1155/2009/905769 Research Article Limit Properties of Solutions of Singular Second-Order Differential Equations Irena Rach ˚unkov ´a,1 Svatoslav Stan ˇek,1 Ewa Weinm ¨uller,2 ... the following system of ordinarydifferential equations: b0t β3 where g ∈ C0, 1 According to 16, the latter system of equations has a continuous solution if and only if the regularity condition ... and/or uniqueness results for solutions of singularboundary value problems2.1 with periodic boundary conditions.3 Linear Singular Equation First, we consider the linear equation, a∈ R \ {0}, ut

Ngày tải lên: 21/06/2014, 20:20

... value problems for second-order differential equations with deviating arguments Some sufficient conditions are formulated under which such problems have quasisolutions or a unique solution A monotone ... upper solutions of (6.11) Thus problem (6.11) has, in segment [y0,z0], the minimal and maximal coupled quasisolutions OnFigure 6.1we see some chosen pairs of numerical approximations of quasisolutions ... yn,zn } To obtain an approximate extremal quasisolutions we can use the elements of sequences { y n,z n } Using numerical methods we can find numerical approximations yn,znofy n,z n, respectively

Ngày tải lên: 22/06/2014, 22:20

... with the numerical solution of delay-differential equations (ĐÉs) Delay-differential equations may best be regarded as extensions of ordinary differential equations(ODÉs) in which the solution ... for ĐÉs include 'ordinary differential equations with time lags' or 'retarded ordinary differential equations' (RODES) A sensible generic term is 'ordinary differential equations with retarded ... delay equations is given This is used in later chapters for stepsize and order control. In section (1.2) we present a brief resume of numerical methods suitable for ordinary differential equations

Ngày tải lên: 11/10/2014, 04:02

... '',qci The Numerical Solution of Delay-differential Equations by David Richard Wile Department of Mathematics University of Manchester ... derivative discontinuities at previous solution pOints or (ii) derivative discontinuities in other solution components. Moreover we showed in equation (1.1.3:12) that the order of continuity for any given ... than or equal to one plus the order of any such effects. That is Ci > min{iz i ,C i } + 1  (1) isi where once again h i denotes a lower bound on the minimum order of any deriva- tive discontinuities

Ngày tải lên: 11/10/2014, 04:03

... property, second order differential operator, continuation theorem, projector, generalized inverse 2010 MSC: 34B10, 34B15 1 Introduction The question of the solvability for nonlinear pertubation of differential ... The equationL x = y has at least one solution defined by x (t) = L−1 P y (t) = Z t 0 (t − s)y(s)ds, t ∈ [0, 1] if and only if γ Z 1 0 (1 − s)y(s)ds + δ Z 1 0 y (s)ds = 0. Example 4.2 (Second order ... analysis Theorem 3.1 LetH =z ∈ Z : i = 0, ∀i ∈ {1, 2, , m} The the equation L x = y has (i) no solution if y /∈ H , (ii) at least one solution defined by x= L−1 P (y) if h ∈ H 4 Examples This section

Ngày tải lên: 14/10/2015, 08:45

... FOR NUMERICAL SOLUTION OF FOR NUMERICAL SOLUTION OF THE mGRLW EQUATION THE mGRLW EQUATION THE mGRLW EQUATION Nguyen Van Tuan Hanoi Metropolitan University Abstract: In this paper, numerical ... B-spline for numerical solution of the modified equal width wave equation”, J Appl Math Inform., Vol 28(3 - 4), pp 611–624 10 A G Kaplan, Y Dereli (2017), “Numerical solutions of the GEW equation ... integer The equation (1) is called the modified generalized regularized long wave (mGRLW) equation If μ = 0, the equation (1) is called the generalized regularized long wave (GRLW) Equation (1)

Ngày tải lên: 13/01/2020, 09:24

... Therefore, the linearized numerical scheme for the MRLW equation is unconditionally  stable.  4 NUMERICAL EXAMPLE We now obtain the numerical solution of the MRLW equation for some problems. To  ... test examples, and the numerical results have been compared with the exact solutions The and in the solutions show the efficiency of the method computationally Keywords: MRLW equation; quartic B ... = b.  Our  numerical  treatment  for  the  MRLW  equation  using  the  collocation  method  with  quartic  B  spline  is  to  find  an  approximate  solution  U(x,t)  to  the  exact  solution 

Ngày tải lên: 28/06/2021, 19:39

... pagesdoi:10.1155/2009/143175 Research Article On the Spectrum of Almost Periodic Solution of Second-Order Neutral Delay Differential Equations with Piecewise Constant of Argument Li Wang and Chuanyi Zhang ... Recommended by Ondrej Dosly The spectrum containment of almost periodic solution of second-order neutral delay differential equations with piecewise constant of argumentEPCA, for short of the ... ft can be constructed by the solutions of corresponding difference equations However, noticing the difference between t and 2t  1/2, the solution of difference equation corresponding to the

Ngày tải lên: 21/06/2014, 20:20

... uniqueness of a periodic solution for second-order ordinary differential equations with some assumption 1 Introduction The study on periodic solutions for ordinary differential equations is a very important ... differential equation theory Many results about the existence of periodic solutions for second-order differential equations have been obtained by combining the classical method of lower and upper solutions ... pagesdoi:10.1155/2011/192156 Research Article Existence and Uniqueness of Periodic Solution for Nonlinear Second-Order Ordinary Differential Equations Jian Zu College of Mathematics, Jilin University, Changchun

Ngày tải lên: 14/07/2023, 09:44

... 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 ... considered to the equivalent Fredholm integral equation of second kind The results significantly extend and improve many known results even for integer-order cases Introduction Fractional calculus ... at least three positive solutions to problem 1.5 For the case of α 2, boundary value problem 1.5 is related to a boundary value problems of integer-order differential equation Feng et al 25 considered

Ngày tải lên: 21/06/2014, 05:20

... positive solution ut ∈ S. Trang 94 Maximal and Minimal Solutions TheoremIn this section, we consider the existence of maximal and minimal solutions for1.2 Definition 4.1 Let mt be a solution ... fractional differential equations with non-monotone term Moreover, the existence of maximal and minimal solutions for the problem is also given 1 Introduction Fractional differential equation can be extensively ... differential equations have been of great interest, and there have been many results on existence and uniqueness of the solution of boundary value problems for fractional differential equations,

Ngày tải lên: 21/06/2014, 07:20

... 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: ... existence of positive solutions; for example, see7,8,11,19,23,24 However, there are few papers investigating the existence of positive solutions of nth impulsive differential equations by using ... and H2 hold Then x ∈ PC n−1 0, 1 ∩ C n J is a solution ofproblem1.3 if and only if x is a solution of the following impulsive integral equation: x t  1 0 H t, sfs, xsds m k1

Ngày tải lên: 21/06/2014, 16:20

... pagesdoi:10.1155/2011/720702 Research Article New Existence Results for Higher-Order Nonlinear Fractional Differential Equation with Integral Boundary Conditions 1 School of Applied Science, Beijing ... paper investigates the existence and multiplicity of positive solutions for a class of higher-order nonlinear fractional differential equations with integral boundary conditions The results are ... equivalent integral equation and applying Krasnoselskii’s fixed-point theorem in cones The nonexistence of positive solutions is also studied 1 Introduction Fractional differential equations arise

Ngày tải lên: 21/06/2014, 16:20

... are derived for all the solutions being oscillating for a class of linear second-order delayed-discrete equations We consider the delayed second-order linear discrete equation Δxn  −pnxn ... oscillation of solutions of first order delay difference equations,” Cubo, vol 7, no 2, pp 223–236, 2005. 14 R Medina and M Pituk, “Nonoscillatory solutions of a second-order difference equation of ... properly cited A linear second-order discrete-delayed equationΔxn  −pnxn − 1 with a positive coefficient p is considered for n → ∞ This equation is known to have a positive solution if p fulfils

Ngày tải lên: 21/06/2014, 18:20

... three-point boundary value problems for nonlinear second-order ordinary differential equations was initiated by Lomtatidze 4,5 Since then, the nonlinear second-order multipoint boundary value problems ... In this paper, we investigate the existence and uniqueness of positive solution for the singular second-order differential equation ut  ft, ut  0, t ∈ 0, 1 1.1 with the m-point boundary ... constructing lower and upper solutions and together with the maximal principle, proved the existence and uniqueness of positive solutions for the following singular second-order m-point boundary value

Ngày tải lên: 21/06/2014, 18:20

... governedby a class of the second-order nonlinear impulsive differential equation in infinite di-mensional spaces Consider the following second-order nonlinear impulsive differential equations: ¨x(t) = ... 1fference EquationsVolume 2007, Article ID 40160, 17 pages doi:10.1155/2007/40160 Research Article Necessary Conditions of Optimality for Second-Order Nonlinear Impulsive Differential Equations ... equations (see [6, Chapter 6]) Recently, Peng and Xiang [11,12] applied the semigroup theory to establish the existence of optimal controls for a class of second-order nonlinear differential equations

Ngày tải lên: 22/06/2014, 19:20