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Analytical Solutions of Some two-point Non-Linear Elliptic Boundary Value Problems

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Applied Mathematics 2012年第9期3卷 1044-1058页

作者： Vembu Ananthaswamy Lakshmanan Rajendran Department of Mathematics The Madura College Madurai India

Several problems arising in science and engineering are modeled by differential equations that involve conditions that are specified at more than one point. The non-linear two-point boundary value problem (TPBVP) (Bratu’s equation, Troesch’s problems) occurs engineering and science, including the modeling of chemical reactions diffusion processes and heat transfer. An analytical expression pertaining to the concentration of substrate is obtained using Homotopy perturbation method for all values of parameters. These approximate analytical results were found to be in good agreement with the simulation results.

关键词： two-point Elliptic Boundary Value Problems Bratu’s Equation Troesch’s Problem Non-Linear Equations Homotopy Perturbation Method Porous Catalyst Numerical Simulation

A two-point Boundary Value Problem by Using a Mixed Finite Element Method

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Applied Mathematics 2015年第12期6卷 1996-2003页

作者： Pedro Pablo Cárdenas Alzate José Rodrigo González Granada Department of Mathematics Universidad Tecnoloacute gica de Pereira Pereira Colombia

This paper describes a numerical solution for a two-point boundary value problem. It includes an algorithm for discretization by mixed finite element method. The discrete scheme allows the utilization a finite element method based on piecewise linear approximating functions and we also use the barycentric quadrature rule to compute the stiffness matrix and the L2-norm.

关键词： two-point BVP Galerkin’s Method Non-Symmetric Problem

A Special Case of Variational Formulation for two-point Boundary Value Problem in L2(Ω)

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Applied Mathematics 2015年第4期6卷 700-706页

作者： Pedro Pablo Cárdenas Alzate Department of Mathematics Universidad Tecnológica de Pereira Pereira Colombia

We consider the nonlinear boundary value problems for elliptic partial differential equations and using a maximum principle for this problem we show uniqueness and continuous dependence on data. We use the strong version of the maximum principle to prove that all solutions of two-point BVP are positives and we also show a numerical example by applying finite difference method for a two-point BVP in one dimension based on discrete version of the maximum principle.

关键词： two-point Boundary Variational Problem Stability Restriction

Several New Types of Fixed point Theorems and Their Applications to two-point Ordinary Differential Equations

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Applied Mathematics 2012年第10期3卷 1109-1116页

作者： Congjun Zhang Jinlu Li Yan Zhang Xiaoliang Feng Department of Mathematics Nanjing University Nanjing Jiangsu People’s Republic of China Department of Mathematics Shawnee State University Portsmouth Ohio USA School of Applied Mathematics Nanjing University of Finance and Economics Nanjing Jiangsu People’s Republic of China

The present paper is mainly concerned with several new types of fixed point theorems in different spaces such as cone metric spaces and fuzzy metric spaces. By using these obtained fixed point theorems, we then prove ... 详细信息

关键词： Expansive Mapping Cone Metric Space Fuzzy Metric Space two-point Ordinary Differential Equations

HIGH ACCURACY FINITE VOLUME ELEMENT METHOD FOR two-point BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

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Numerical Mathematics A Journal of Chinese Universities(English Series) 2002年第2期11卷 213-225页

作者： Wang Tongke(王同科) School of Mathematics and System Science Shandong Univerisity Jinan 250100 PRC/School of Mathematics and information Science Henan Normal University Xinxiang 453002 PRC

In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference methods. It is proved that the method has optimal order error estimate O(h3) in H1 norm. Finally, two examples show that the method is effective.

关键词： second order ordinary differential equation, two-point boundary value problem,high accuracy, finite volume element method, error estimate.

ASYMPTOTIC ERROR EXPANSIONS OF QUADRATIC SPLINE COLLOCATION SOLUTIONS FOR two-point BOUNDARY VALUE PROBLEMS

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Numerical Mathematics A Journal of Chinese Universities(English Series) 1994年第2期3卷 120-125页

作者：韩国强 Department of Computer Science South China University of Technology Guangzhou 510641 PRC.

In this paper, we consider the following problem:The quadratic spline collocation, with uniform mesh and the mid-knot points are taken as the collocation points for this problem is considered. With some assumptions, we have proved that the solution of the quadratic spline collocation for the nonlinear problem can be written as a series expansions in integer powers of the mesh-size parameter. This gives us a construction method for using Richardson’s extrapolation. When we have a set of approximate solution with different mesh-size parameter a solution with high accuracy can he obtained by Richardson’s extrapolation.

关键词： Asymptotic error expansion quadratic spline collocation method two-point boundary value problem Richardson’s extrapolation.

Numerical Solution of Singularly Perturbed two-point Boundary Value Problem via Liouville-Green Transform

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American Journal of Computational Mathematics 2013年第1期3卷 1-5页

作者： Hradyesh Kumar Mishra Sonali Saini Department of Mathematics Jaypee University of Engineering & Technology Guna India

In this paper, authors describe a Liouville-Green transform to solve a singularly perturbed two-point boundary value problem with right end boundary layer in the interval [0, 1]. They reply Liouville-Green transform into original given problem and finds the numerical solution. Then they implemented this method on two linear examples with right end boundary layer which nicely approximate the exact solution.

关键词： Singular Perturbation Ordinary Differential Equation Boundary Layer two-point Boundary Value Problem Liouville-Green Transform

Relationship between wall shear stresses and streamwise vortices in turbulent flows over wavy boundaries

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Applied Mathematics and Mechanics(English Edition) 2019年第3期40卷 381-396页

作者： Lihao WANG Weixi HUANG Chunxiao XU Lian SHEN Zhaoshun ZHANG Applied Mechanics Laboratory Department of Engineering MechanicsTsinghua University Department of Mechanical Engineering and Saint Anthony Falls Laboratory University of Minnesota

The relationship between wall shear stresses and near-wall streamwise vortices is investigated via a direct numerical simulation(DNS) of turbulent flows over a wavy boundary with traveling-wave motion. The results indicate that the wall shear stresses are still closely related to the near-wall streamwise vortices in the presence of a wave. The wave age and wave phase significantly affect the distribution of a two-point correlation coefficient between the wall shear stresses and streamwise vorticity. For the slow wave case of c/Um = 0.14, the correlation is attenuated above the leeward side while the distribution of correlation function is more elongated and also exhibits a larger vertical extent above the crest. With respect to the fast wave case of c/U_m=1.4, the distribution of the correlation function is recovered in a manner similar to that in the flat-wall case. In this case, the maximum correlation coefficient exhibits only slight differences at different wave phases while the vertical distribution of the correlation function depends on the wave phase.

关键词： direct numerical simulation(DNS) wall shear stress near-wall streamwise vortex two-point correlation

Numerical solutions for point masses sliding over analytical surfaces: Part 2

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Theoretical & Applied Mechanics Letters 2019年第2期9卷 96-105页

作者： Stefano Tinti Glauco Gallotti Department of Physics and Astronomy University of Bologna

This paper is the second of two companion papers addressing the dynamics of two coupled masses sliding on analytical surfaces and interacting with one another. The motion occurs under the effect of gravity, the reaction force of the surface and basal friction. The interaction force maintains the masses at a fixed distance and lies on the line connecting them. The equations of motion form a system of ordinary differential equations that are solved through a fourth-order Runge–Kutta numerical scheme. In the first paper we considered an approximate method holding when the line joining the masses is almost tangent to the surface at the instant mass positions. In this second paper we provide a general solution. Firstly, we present special cases in which the system has exact solutions. Second, we consider a series of numerical examples where the interest is focused on the trajectories of the masses and on the intensity and changes of the interaction force.

关键词： two-point system Rigid-body motion Sliding downslopes