spectral methods for initial value problems

... 45 Testing 5.1 General tests 5.2 Linear problems 5.2.1 Constant coefficient problems 5.2.2 Time-dependent problems 5.3 Nonlinear problems ... directory gnuplot file for generating the plot in Figure 3.3 matlab code for the DETEST E1 problem gnuplot file for generating the plots in Figure 3.4 gnuplot file for generating the plots ... Figure 3.5 gnuplot file for generating the plots in Figure 3.6 gnuplot file for generating the plots in Figure 3.7 gnuplot file for generating the plots in Figure 3.8 gnuplot file for generating the...

Ngày tải lên: 12/01/2014, 22:07

... continuous case is always of index for all t ∈ J, while for n 1, {An ,Bn } is not necessarily of index Now, we describe shortly the decomposition technique for index LIDEs Performing Pn G−1 and Qn G−1 ... uniformly bounded inγn for all n 0, y,x ∈ Rm ; verses, that is, G−1 (y,x) n (iii) hn (y,x) = hn (Pn y,x) for all n 0, y,x ∈ Rm ; ¯ ¯ ¯ ¯ ¯ ¯ (iv) hn (y,x) − hn ( y , x) Ln ( y − y + x − x )1/2 for ... Guoping for their hospitality during his visit to the Institute of Mathematics, Chinese Academy of Sciences References [1] [2] [3] [4] P K Anh and L C Loi, On multipoint boundary -value problems for...

Ngày tải lên: 23/06/2014, 00:20

... 2.1 2.2 2.3 Problems for Equations Problems for Equations of Hyperbolic Type Inverse problems for x-hyperbolic systems Inverse problems for t-hyperbolic systems Inverse problems for hyperbolic ... 8.2 8.3 Problems for Equations of Second Order Cauchy problem for semilinear hyperbolic equations Two-point inverse problems for equations of hyperbolic type Two-point inverse problems for equations ... Inverse problems for equations in a Banach space correspond to abstract forms of inverse problems for partial differential equations The methodof differential equations in a Banachspace for investigating...

Ngày tải lên: 17/03/2014, 14:30

... for all x ∈ C, for a constant κ > 1; then, T is relaxed μ, ν -cocoercive and Lipschitz continuous Especially, T is ν-strong monotone Proof Since T x κx, for all x ∈ C, we have T : C → C For for ... Preliminaries For solving the equilibrium problem for a bifunction F : C × C → R, let us assume that F satisfies the following conditions: A1 F x, x for all x ∈ C; A2 F is monotone, that is, F x, y A3 for ... inequality For the recent applications, sensitivity analysis, dynamical systems, numerical methods, and physical formulations of the variational inequalities, see 1–24 and the references therein For...

Ngày tải lên: 21/06/2014, 07:20

... “Boundary value problems for functional differential systems,” Indian Journal of Pure and Applied Mathematics, vol 36, no 12, pp 685–705, 2005 X Deng and H Shi, “On boundary value problems for second ... boundary value problems with sign changing nonlinearities,” Journal of Computational and Applied Mathematics, vol 169, no 2, pp 345–357, 2004 J Henderson and A Peterson, “Boundary value problems for ... t∈ 1,T we obtain for s ∈ τ ys τ Lemma 3.2 For every y ∈ K, there is t0 ∈ τ yt0 ≥ ≥ m y , M 3.9 1, T m y M 3.10 1, T , such that τ y 3.11 12 Proof For s ∈ τ have Boundary Value Problems 1, T ,...

Ngày tải lên: 21/06/2014, 11:20

... 2.2 exists for each x, y ∈ U It is also said to be uniformly smooth if the limit is attained uniformly for x, y ∈ U It is well known that p and Lp < p < ∞ are uniformly convex and uniformly smooth; ... Applications It is obvious that 2.6 holds for N 1, see 34 for more details Next, we assume that 2.6 is true for N − It remains to show that 2.6 holds for N We observe that N i ω xi ω N xN 1−ω ... following conditions: i αn < for all n ∈ N ∪ {0} and lim supn → ∞ αn < 1, ii βn i for all i 1, 2, , N i 1 a lim infn → ∞ βn βn b limn → ∞ βn 1, > for all i and N i i βn for all n ∈ N ∪ {0} If either...

Ngày tải lên: 21/06/2014, 23:20

... operator and satisfies one of the following two conditions: x for x ∈ K ∩ ∂Ω1 , Ψx ≥ x for x ∈ K ∩ ∂Ω2 ; (1) Ψx x for x ∈ K ∩ ∂Ω2 , Ψx ≥ x for x ∈ K ∩ ∂Ω1 (2) Ψx Then Ψ has a fixed point in K ∩ (Ω2 ... y(1) for t ∈ [−τ,0], α0 + α1 (2.8) β1 − β0 y for t ∈ [1,T + 2] β1 (T + 1) Then E is a Banach space endowed with norm · and K is a cone in E For y ∈ K, we have y(t) = (α1 /(α0 + α1 ))y(1) for ... τ }, such that for ϕn f ϕ(n),ϕn m ϕn τ p −1 τ ≥ N, (3.17) Let ρ2 = N + h τ α0 + m−1 max m ρ2 + h τ , Φq max f ϕ(n),ϕn : ϕn α0 τ ρ2 + h τ α0 (3.18) 10 Boundary Value Problems For y ∈ K ∩ ∂Ωρ2...

Ngày tải lên: 22/06/2014, 19:20

... established for all the eigenvalues of the systems (1.3) and (1.4) under certain conditions Note that the problems (1.3) and (1.4) are discrete analogies to the following boundary value problems for ... Travis [7] established some comparison results for the smallest eigenvalues of two eigenvalue problems for boundary value problems of 2nth-order linear differential equations, by using the theory ... fourth order nonlinear boundary value problems, Applicable Analysis 74 (2000), no 1-2, 201–214 [5] D Hankerson and A Peterson, Comparison theorems for eigenvalue problems for nth order differential...

Ngày tải lên: 22/06/2014, 22:20

... and solution methods for some important problems in fluid dynamics are discussed, such as transonic flows for compressible inviscid fluids and the Navier-Stokes equations viii Preface for incompressible ... possibilities of the solution methods discussed in Chapter VII, which also contains an introduction to arc-lengthcontinuation methods (H B Keller) for solving nonlinear boundary -value problems with multiple ... which may be helpful for solving elliptic boundary -value problems with large first-order terms Finally, Appendix III, which contains various information and results useful for the practical solution...

Ngày tải lên: 27/06/2014, 18:20

... paper we proposed three parallel hybrid extragradients methods for finding a common element of the set of solutions of equilibrium problems for pseudomonotone M bifunctions {fi }N i=1 and the set ... National Foundation for Science and Technology Development for a financial support References [1] P.N Anh, A Hybrid Extragradient Method Extended to Fixed Point Problems and Equilibrium Problems, Optimization ... Parallel hybrid methods for a finite family of relatively nonexpansive mappings Numer Funct Anal Optim 35(6) (2014), pp 649-664 [3] P.K Anh, D.V Hieu, Parallel and sequential hybrid methods for a finite...

Ngày tải lên: 14/10/2015, 08:21

... for obtaining the spectral solution of a special family of fractional initial value problems using a pseudo -spectral method, and Pedas and Tamme [25] developed the spline collocation method for ... derivatives and used together spectral methods for solving FDEs with initial and boundary conditions respectively In [18,22,23], the authors have presented spectral tau method for numerical solution ... formulation, there are three most common spectral schemes, namely, the collocation, Galerkin and tau methods Spectral methods have been applied successfully to numerical simulations of many problems...

Ngày tải lên: 21/06/2014, 17:20

... Springer, New York, NY, USA, 1990 Boundary Value Problems 23 14 R Landes, “On the existence of weak solutions for quasilinear parabolic initial- boundary value problems, ” Proceedings of the Royal Society ... Models and Finite Elements for Reservoir Simulation, NorthHolland, Amsterdam, The Netherlands, 1986 W X Shen and S M Zheng, “Nonlocal initial- boundary value problems for nonlinear parabolic equations,” ... approximation, 2.6 holds for any h ∈ W 1,∞ R with compact support and all 0} ξ ∈ {ξ ∈ L2 0, T ; V | ξt ∈ L2 Q , ξ ·, T Boundary Value Problems Now we can state the existence result for prolem P as follows...

Ngày tải lên: 21/06/2014, 20:20

... Nonpositone discrete boundary value problems, Nonlinear Anal 39 (2000), no 2, 207–215 R P Agarwal, D O’Regan, and V Lakshmikantham, Existence criteria for singular initial value problems with sign changing ... singular discrete boundary value problems for the one-dimensional p-Laplacian, to appear in J Appl Anal H L¨ and C Zhong, A note on singular nonlinear boundary value problems for the oneu dimensional ... 2.1 guarantees that (2.23) has a solution u ∈ C(N + , R) with u(k) > for k ∈ N Next we present a result for initial value problems Theorem 2.3 Let n0 ∈ {1,2, } be fixed and suppose (1.2), (1.3)...

Ngày tải lên: 23/06/2014, 00:20

Ngày tải lên: 08/05/2014, 12:49

... 0, 𝑐2 ∕= 0, (1.3) the problems are two-point BVPs; if 𝑏1 = 𝑐1 = 𝑎2 = 𝑏2 = 0, the problems are initial value problems; if 𝑏1 = 𝑎2 = 0, 𝑎1 = 𝑐1 ∕= 0, 𝑏2 = 𝑐2 ∕= 0, (1.4) the problems are periodic ... Positive solutions for nonlinear discrete periodic boundary value problems Comput Math Appl 59, 136–141 (2010) [6] Russell, R.D., Shampine, L.F.: A collocation method for boundary value problems Numer ... Classification (2000) 35A24, 46E20, 47B32 Preprint submitted to Boundary Value Problems December 7, 2011 Introduction Initial and boundary value problems of ordinary differential equations play an important...

Ngày tải lên: 20/06/2014, 20:20

... boundary value problems for p-Laplacian dynamic equations on time scales J Math Anal Appl 321, 911–920 (2006) 16 Hong, S: Triple positive solutions of three-point boundary value problems for p-Laplacian ... boundary value problems of ordinary differential equations (BVPs for short) arise in a variety of different areas of applied mathematics and physics For example, the vibrations of a guy wire of a uniform ... i=1 which means that for u ∈ ∂Ωr ∩ P, Au ≤ u On the other hand, for u ∈ P, in view of Lemma 2.8, there holds u(t) ≥ ξ1 T u , for t ∈ [ξ1 , T ] Denote Ωρ = {u ∈ E, u < ρ} Then for u ∈ ∂Ωρ ∩ P, considering...

Ngày tải lên: 20/06/2014, 20:20

... value problems with integral boundary conditions on time scales also cover two-point, three-point, , n-point boundary problems as the nonlocal boundary value problems in the continuous case For ... boundary value problems for some dynamic equations on time scales Math Comput Modell 49, 1386–1393 (2009) doi:10.1016/j.mcm.2009.01.001 Zhang, X, Ge, W: Positive solutions for a class of boundary -value ... of 18 problems with integral boundary conditions constitute a very interesting and important class of problems They include two-point, three-point, multipoint and nonlocal boundary value problems...

Ngày tải lên: 20/06/2014, 22:20

... Boundary Value Problems This section is devoted to the study of the second order boundary value problem (BVP) Heikkilä Boundary Value Problems 2011, 2011:24 http://www.boundaryvalueproblems.com/content/2011/1/24 ... equality holds for some n Î N, then x* = Gn-1(x+) is the greatest fixed point of G in [x-, x+] First order initial value problems In this section, existence and comparison results are derived for the ... Heikkilä Boundary Value Problems 2011, 2011:24 http://www.boundaryvalueproblems.com/content/2011/1/24 Page of 19 Proposition 3.2 Assume that g(x) is RP integrable on [a, b] for every x ∈ L1 (a,...

Ngày tải lên: 20/06/2014, 22:20

... for boundary value problems of nonlinear fractional differential equation Nonlinear Anal 71, 5545–5550 (2009) doi:10.1016/j.na.2009.04.045 16 Zhang, S: Positive solutions for boundary -value problems ... Furthermore, denote K P,Q = KP (I - Q)N and for ≤ t

Ngày tải lên: 21/06/2014, 00:20