— application of finite difference method for solving boundary value problems

... al Boundary Value Problems 2011, 2011:3 http://www.boundaryvalueproblems.com/content/2011/1/3 Page of decomposition method [15-17], differential transform method [18], variational iteration method ... Motsa et al Boundary Value Problems 2011, 2011:3 http://www.boundaryvalueproblems.com/content/2011/1/3 Page of Table Order [i, m] ISHAM approximate results for f“ (0) of the Blasius boundary layer ... Motsa et al Boundary Value Problems 2011, 2011:3 http://www.boundaryvalueproblems.com/content/2011/1/3 Page of Table Order [m, m] ISHAM approximate results for f“ (0) of the Falkner-Skan boundary...

Ngày tải lên: 21/06/2014, 02:20

... a mimetic method for the steady state diffusion equations The original idea of introducing (4.1) as a mimetic method for Poisson equation was given in [7] However, a rigorous proof of its convergence ... described Then, in Section we present the proof of the quadratic convergence rate of the new method Next, the solution and analysis of illustrative numerical test problems are given in Section Finally, ... equations for the new mimetic method (4.1), which represents an n + × n + linear system Its first equation represents the discretization of the boundary condition given by (2.2a), it is of the form...

Ngày tải lên: 22/06/2014, 19:20

... (strong form) and weak form 28 2.2 Finite element method 31 2.2.1 Discretization by finite elements 31 2.2.2 An error estimation of FEM 32 2.2.3 Matrix form of the ... forces on the surface of interaction At low frequencies (up to hundreds of KHz) analytical solutions of this type of problems exits only for certain simple configurations For problems where geometry ... convergence rate of the standard finite element method for pure mechanical problems (only a mechanical field) In this thesis, ES-FEM is further extended for the electromechanical coupling problems with...

Ngày tải lên: 26/08/2015, 13:34

... employment of a special algorithm for each of the term Similar to Forward Euler method for solving differential equation numerically, the splitting scheme is also a first order accurate method To ... simple formula, there are unfortunately serious problems with this Forward Euler method Firstly, the Forward Euler has been proven to be unconditionally unstable for the discretization of the ... had to take care of the boundary values of the advected result Here we choose to set the boundary values to zeros because the fluid cannot flow at the boundary The routine SetBoundaryZero will...

Ngày tải lên: 12/10/2015, 17:35

... projection method for finding a common element of the set of solutions of the generalized mixed equilibrium problems, the set of the variational inequality and the set of common fixed points for a ... strong convergence theorem for finding a common element of the set of solutions for a generalized equilibrium problem (1.4) and the set of common fixed points for a pair of relatively nonexpansive ... 78:29-41 Jitpeera T, Kumam P: An extragradient type method for a system of equilibrium problems, variational inequality problems and fixed points of finitely many nonexpansive mappings J Nonlinear...

Ngày tải lên: 21/06/2014, 02:20

... scales,” Boundary Value Problems, vol 2011, Article ID 198598, 15 pages, 2011 12 J Henderson, “Multiple solutions for 2m order Sturm-Liouville boundary value problems on a measure chain,” Journal of ... dynamic boundary value problems with mixed derivatives,” Advances in Difference Equations, vol 2006, Article ID 54989, 15 pages, 2006 C J Chyan and J Henderson, “Twin solutions of boundary value problems ... 70901016 , HSSF of Ministry of Education of China no 09YJA790028 , Program for Innovative Research Team of Liaoning Educational Committee no 2008T054 , and Innovation Method Fund of China no 2009IM010400-1-39...

Ngày tải lên: 21/06/2014, 05:20

... value problems on time scales,” Journal of Mathematical Analysis and Applications, vol 289, no 1, pp 110–125, 2004 26 Z He, “Existence of two solutions of m-point boundary value problem for second ... and X Jiang, “Triple positive solutions of boundary value problems for p-Laplacian dynamic equations on time scales,” Journal of Mathematical Analysis and Applications, vol 321, no 2, pp 911–920, ... Otero-Espinar, “Existence and approximation of solution of three-point boundary value problems on time scales,” Journal of Difference Equations and Applications, vol 14, no 7, pp 723–736, 2008...

Ngày tải lên: 21/06/2014, 20:20

Ngày tải lên: 31/03/2014, 15:23

... characteristic value of T if there exists v Î E, v ≠ 0, such that v = μTv, i.e., μ-1 is a nonzero eigenvalue of T Let r(T) denote the set of real characteristic values of T and Γ denote the closure of the ... discuss the existence of principal eigenvalues for the BVP (1.3) and (1.4) At first, we give the definition of principal eigenvalue of (1.3) and (1.4) Definition 3.1 An eigenvalue l for (1.3) and (1.4) ... nonlinear eigenvalue problems for third order difference equations Comput Math Appl 36(10-12), 347–355 (1998) doi:10.1016/S0898-1221(98)80035-7 Agarwal, RP, O’Regan, D: Boundary value problems for discrete...

Ngày tải lên: 20/06/2014, 20:20

... characteristic value of T if there exists v Î E, v ≠ 0, such that v = μTv, i.e., μ-1 is a nonzero eigenvalue of T Let r(T) denote the set of real characteristic values of T and Γ denote the closure of the ... discuss the existence of principal eigenvalues for the BVP (1.3) and (1.4) At first, we give the definition of principal eigenvalue of (1.3) and (1.4) Definition 3.1 An eigenvalue l for (1.3) and (1.4) ... nonlinear eigenvalue problems for third order difference equations Comput Math Appl 36(10-12), 347–355 (1998) doi:10.1016/S0898-1221(98)80035-7 Agarwal, RP, O’Regan, D: Boundary value problems for discrete...

Ngày tải lên: 21/06/2014, 17:20

... in 1–5 Proof of Main Results 2.1 Some Lemmas Lemma 2.1 Consider the following eigenvalue problem −u τu t , u u t ∈ 0, , 2.1 Boundary Value Problems Then the eigenvalues are mπ τm for m 1, 2, ... t ∈ 0, , ψ t, ω t ω ω for t ∈ 0, , 2.15 Boundary Value Problems Next we consider the boundary value problem −u a t ut t ∈ 0, , f t, u 0 u 1, 2.16 where a, f ∈ M, a t ≥ for t ∈ 0, Lemma 2.4 The ... g2 t, ω t ut ω for t ∈ 0, , e t 0, for t ∈ 0, , n ∈ N, for t ∈ 0, , lim ωn t ω t β u t β ω e t 2.50 for t ∈ 0, , Next we consider the boundary value problem −vn t λh2 t, ωn vn for t ∈ 0, , 2.51...

Ngày tải lên: 21/06/2014, 20:20

... been continued in [5] for nth-order periodic boundary value problems, in [11] for antiperiodic dynamic equations, and in [1] for second-order dynamic equations with dependence of the nonlinear term ... functional boundary conditions, Computers & Mathematics with Applications 42 (2001), no 3–5, 593– 601 , Extremal solutions and Green’s functions of higher order periodic boundary value problems ... and Applications 247 (2000), no 1, 67– 86 , Existence and comparison results for difference φ-Laplacian boundary value problems with [8] lower and upper solutions in reverse order, Journal of Mathematical...

Ngày tải lên: 22/06/2014, 22:20

... the application of such techniques for the formulation of certain heat and fluid flow problems The problems presented here provide a valuable basis for the discussion of the finite element method ... Fundamentals of the Finite Element Method for Heat and Fluid Flow Fundamentals of the Finite Element Method for Heat and Fluid Flow Roland W Lewis University of Wales Swansea, UK Perumal ... • The thermal force vector consists of known values The method of assembly can be extended to more than two layers of insulation • The effect of natural boundary conditions (flux boundary conditions)...

Ngày tải lên: 17/03/2014, 13:53

... number of corresponding mesh points Three-point boundary value problems have been studied extensively in the literature For a discussion of existence and uniqueness results and for applications of ... consists of using a class of special piecewise uniform meshes a Shishkin mesh , see, e.g., 4–8 for motivation for this type of mesh , which are constructed a priori in function of sizes of parameter ... numerical methods to these problems, whose accuracy does not depend on the parameter value ε; that is, methods that are convergence ε-uniformly 1–5 One of the simplest ways to derive such methods...

Ngày tải lên: 21/06/2014, 11:20

... has a unique solution c1 c2 Therefore v t ≡ w t for t ∈ −τ, T This completes the proof of the uniqueness of the solution 10 Boundary Value Problems Existence of Positive Solutions In this section, ... Shi, and D C Zhang, “Existence of positive solutions for boundary value problems of nonlinear functional difference equation with p-Laplacian operator,” Boundary Value Problems, vol 2007, Article ... Boundary value problems for functional-differential equations,” Journal of Mathematical Analysis and Applications, vol 199, no 1, pp 213–230, 1996 F.-H Wong, “Existence of positive solutions for...

Ngày tải lên: 21/06/2014, 11:20

... ∂2 ∂x 3.1 Boundary Value Problems Then, there exists a monotone sequence {αn } of approximate solutions converging uniformly to a unique solution of the problems 1.1 - 1.2 Proof For y ∈ R, ... Methods & Applications, vol 64, no 6, pp 1271–1277, 2006 D Jiang, J J Nieto, and W Zuo, “On monotone method for first and second order periodic boundary value problems and periodic solutions of ... quasilinearization method for Neumann problems, ” Journal of Mathematical Analysis and Applications, vol 257, no 2, pp 356–363, 2001 14 P W Eloe and Y Gao, “The method of quasilinearization and a three-point boundary...

Ngày tải lên: 21/06/2014, 11:20

... and convex subset of C of a Hilbert space H We denote by A the set of solutions of 4.1 and assume that A / ∅ We denote the sets of solutions of the following two optimization problems by A1 and ... W Takahashi, “Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces,” Journal of Mathematical Analysis and Applications, vol 331, no 1, pp 506–515, ... iteration scheme with perturbed mapping for equilibrium problems and fixed point problems of finitely many nonexpansive mappings,” Journal of Optimization Theory and Applications, vol 139, no 2, pp 403–418,...

Ngày tải lên: 21/06/2014, 11:20

... ∈ V I C, B For finding a common element of the set of fixed points of a nonexpansive mapping and Fixed Point Theory and Applications the set of solution of variational inequalities for β-inverse-strongly ... element of the set of solutions of the equilibrium problem 1.13 , the set of common fixed points of infinitely family nonexpansive mappings, and the set of solutions of variational inequality 1.1 for ... “An extragradient approximation method for equilibrium problems and fixed point problems of a countable family of nonexpansive mappings,” Fixed Point Theory and Applications, vol 2008, Article...

Ngày tải lên: 21/06/2014, 20:20

... Ax, x − h x , γf for all x ∈ H where h is a potential function for γf i.e., h x Journal of Inequalities and Applications For finding a common element of the set of fixed points of nonexpansive ... “Viscosity approximation methods for fixed-points problems, ” Journal of Mathematical Analysis and Applications, vol 241, no 1, pp 46–55, 2000 H K Xu, “Viscosity approximation methods for nonexpansive ... theorem for a common fixed point of nonexpansive mapping and strictly pseudocontractive mapping Moreover, we consider the problem of finding a common element of the set of fixed points of nonexpansive...

Ngày tải lên: 22/06/2014, 02:20

... many papers on the existence of solutions for p-Laplacian boundary value problems via subsuper solution method see 20–24 But results on the sub-super-solution method for p x -Laplacian equations ... contradiction to the definition of t0 , so u t ≤ β t , for any t ∈ T1 , T2 Proofs of main results In this section, we will deal with the proofs of main results Proof of Theorem 1.1 From Lemmas 2.5 ... -Laplacian system boundary value problems, ” Journal of Mathematical Analysis and Applications, vol 327, no 1, pp 127–141, 2007 13 Q Zhang, “Existence of positive solutions for a class of p x -Laplacian...

Ngày tải lên: 22/06/2014, 03:20