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In this paper, a novel weak form quadrature element method (QEM) is proposed for accurate free transverse vibration analysis of thin isotropic skew plates with general boundary conditions. In the formulation of the stiffness matrix, the first and second order derivatives of the shape functions at integration points are computed explicitly by using the differential quadrature rule. This leads to a great simplicity in formulating an N × N -node quadrature plate element and a large reduction of programming effort. Different from the existing weak form quadrature element method or differential quadrature finite element method, the element nodes can be either the same or different from the integration points. Convergence studies are performed. Free vibration of skew thin plates with various skew angles and different combinations of boundary conditions is analyzed. It is shown that although the assumed displacement field does not explicitly consider the bending moment singularities at the obtuse angles, the proposed QEM can yield accurate frequencies even for the thin isotropic skew plate with large skew angles. [ABSTRACT FROM AUTHOR]

Abstract: The singular boundary value problem is studied in this paper.The singularity may appear at and the function may be superlinear at and change sign. The existence of solutions is obtained via an upper and lower solutions method. [Copyright &y& Elsevier]

Abstract: Determination of an unknown time-dependent function in parabolic partial differential equations, plays a very important role in many branches of science and engineering. In the current investigation, the Adomian decomposition method is used for finding a control parameter in the quasilinear parabolic equation , in with known initial and boundary conditions and subject to an additional condition in the form of which is called the boundary integral overspecification. The main approach is to change this inverse problem to a direct problem and then solve the resulting equation using the well known Adomian decomposition method. The decomposition procedure of Adomian provides the solution in a rapidly convergent series where the series may lead to the solution in a closed form. Furthermore due to the rapid convergence of Adomian’s method, a truncation of the series solution with sufficiently large number of implemented components can be considered as an accurate approximation of the exact solution. This method provides a reliable algorithm that requires less work if compared with the traditional techniques. Some illustrative examples are presented to show the efficiency of the presented method. [Copyright &y& Elsevier]

Abstract: In this paper, we study the existence of three positive solutions for the second-order two-point boundary value problem on a measure chain, where is continuous and a nonnegative function that is allowed to vanish on some subintervals of of the measure chain. The method involves applications of a new fixed-point theorem due to Bai and Ge [Z.B. Bai, W.G. Ge, Existence of three positive solutions for some second order boundary-value problems, Comput. Math. Appl. 48 (2004) 699–707]. The emphasis is put on the nonlinear term involved with the first order delta derivative . [Copyright &y& Elsevier]

Abstract: By a new approach, we present a new existence result of positive solutions to the following Dirichlet boundary value problem, It is remarkable that the result of this paper is not obtained by employing the fixed-point theorems in cone and the method of the lower and upper functions. Our nonlinearity may change sign and be singular at t = 0, 1, χ = 0. [Copyright &y& Elsevier]

Abstract: Singularly perturbed self-adjoint boundary-value problems are considered in this article. A difference scheme based on quintic spline is proposed. This scheme is applied to the subproblems obtained from the given problem by dividing the whole domain into nonoverlapping subdomains. The proposed scheme is of fourth-order convergent and more suitable for parallel computers. Stability and convergence of the method are discussed. Numerical examples are provided to show the efficiency and accuracy. [Copyright &y& Elsevier]

Abstract: This paper considers the existence of extreme solutions of the periodic boundary value problems for the second order functional differential equations. The novelty is that we introduce a new concept for lower and upper solutions and present that the method of lower and upper solutions coupled with monotone iterative technique is still valid. Meanwhile, we extend previous results. [Copyright &y& Elsevier]

Abstract: In this paper, we study the existence of positive solution for two classes of nonlinear second-order three-point boundary value problems using some monotone iterative schemes. In both cases, such schemes start off with known constant functions and, therefore, are useful to computation purpose. [Copyright &y& Elsevier]

Abstract: This paper introduces radial basis functions (RBF) into the collocation methods and the combined methods for elliptic boundary value problems. First, the Ritz-Galerkin method (RGM) is chosen using the RBF, and the integration approximation leads to the collocation method of RBF for Poisson''s equation. Next, the combinations of RBF with finite-element method (FEM), finite-difference method (FDM), etc., can be easily formulated by following Li [1] and Hu and Li [2,3], but more analysis of inverse estimates is explored in this paper. Since the RBFs have the exponential convergence rates, and since the collocation nodes may be scattered in rather arbitrary fashions in various applications, the RBF may be competitive to orthogonal polynomials for smooth solutions. Moreover, for singular solutions, we may use some singular functions and RBFs together. Numerical examples for smooth and singularity problems are provided to display effectiveness of the methods proposed and to support the analysis made. [Copyright &y& Elsevier]

Abstract: This paper discusses the antiperiodic boundary value problem for first-order impulsive ordinary differential equations. We establish several existence results by using the Leray-Schauder alternative, the lower and upper solution method and the monotone iterative technique. [Copyright &y& Elsevier]

The periodical boundary value problem for linear second-order ordinary differential equation with small parameter by the first and second derivatives is considered. By the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with weight and remainder term in integral form, an exponentially fitted difference scheme is constructed in a uniform mesh which gives first-order uniform convergence in the discrete maximum norm. Numerical experiments support these theoretical results. [Copyright &y& Elsevier]

In this paper, the existence of at least three positive solutions for the boundary value problem (BVP) of second-order functional differential equation with the form y″(t) + f(t, yt) = 0, for t ∊ [0,1], αy(t) -βy′(t) =η(t), for t ∊ [−τ,0], −γy(t) + Δy′(t) = ζ(t), for t ∊ [1, 1 + a], is studied. Moreover, we investigate the existence of at least three partially symmetric positive solutions for the above BVP with αΔ = βγ. [Copyright &y& Elsevier]