REFINED DIFFERENTIAL EQUATIONS OF DEFLECTIONS IN AXIAL SYMMETRICAL BENDING PROBLEMS OF SPHERICAL SHELL AND THEIR SINGULAR PERTURBATION SOLUTIONS

This paper deals with the research of accuracy of differential equations of deflections. The basic idea is as follows. Firstly, considering the boundary effect the meridian midsurface displacement u=0, thus we derive the deflection differential equations; secondly we accurately prove that by use of the deflection differential equations or the original differential equations the same inner forces solutions are obtained; finally, we accurately prove that considering the boundary effect the meridian surface displacement u = 0 is an exact solution. In this paper we give the singular perturbation solution of the deflection differential equations. Finally we check the equilibrium condition and prove the inner forces solved by perturbation method and the outer load are fully equilibrated. It shows that perturbation solution is accurate. On the other hand, it shows again that the deflection differential equation is an exact equation.The features of the new differential equations are as follows:1. The accuracies of the new differential equations and the original differential e-quations are the same.2. The new differential equations can satisfy the boundary conditions simply.3. It is advantageous to use perturbation method with the new differential equations.4 We may obtain the deflection expression(w)and slope expression (dw/da) by using the new differential equations.The new differential equations greatly simplify the calculation of spherical shell. The notation adopted in this paper is the same as that in Ref. [1]

SINGULAR PERTURBATION SOLUTIONS OF THE NONLINEAR STABILITY OF A TRUNCATED SHALLOW SHPERICAL SHELL UNDER LINEAR DISTRIBUTED LOADS ALONG THE INTERIOR EDGE

Using a singular perturbation method, the nonlinear stability of a truncated shallow, spherical shell without a nondeformable rigid body at the center under linear distributed loads along the interior edge is investigated in this paper. When the geometrical parameter k is large, the uniformly valid asymptotic solutions are obtained.

ASYMPTOTIC SOLUTION OF SINGULAR PERTURBATION PROBLEMS FOR THE FOURTH-ORDER ELLIPTIC DIFFERENTIAL EQUATIONS

In this paper we consider the singularly perturbed boundary value problem for the fourth-order elliptic differential equation, establish the energy estimates of the solutionand its derivatives and construct the formal asymptotic solution by Lyuternik- Vishik 's method. Finally, by means of the energy estimates we obtain the bound of the remainder of the asymptotic solution.

ASYMPTOTIC SOLUTION FOR SINGULAR PERTURBATION PROBLEMS OF DIFFERENCE EQUATION

In this paper, we constructed a new asymptotic method for singular perturbation problems of difference equation with a small parameter.

SINGULAR PERTURBATION OF INITIAL BOUNDARY VALUE FROBLEMS OF REACTION DIFFUSlON EQUATION WITH DELAY

In this paper we consider the initial-boundary value problems for a class ofapplications, such as biomathematics and biochemistry.Applying the method ofcomposile expansion we construct the formally asymptotic solution of the problemdescribed. With the help of theory of upper and lower solutions we prove the uniformlyvalidity of the formal solution and the existence of solution of the original problem.

UNIQUENESS OF SOLUTIONS OF SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR THIRD QRDER NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS

By making use of the differential inequalities, in this paper we study the uniqueness of solutions of the two kinds of the singularly perturbed boundary value problems for the nonlinear third order ordinary differential equation with a small parameter ε>0: where i=1, 2; a(?)(ε), β(ε) and γ(ε) are functions defined on (0, ε_o], while ε_o>0 is a constant.This paper is the continuation of our works [4, 6].

NUMERICAL SOLUTION OF QUASILINEAR SINGULARLY PERTURBED ORDINARY DIFFERENTIAL EQUATION WITHOUT TURNING POINTS

In this paper we consider a quasilinear second order ordinary diferential equation with a small parameter Firstly an approximate problem is constructed. Then an iterative procedure is developed. Finally we give an algorithm whose accuracy is good for arbitrary e>0 .

NUMERICAL SOLUTION OF THE SINGULARLY PERTURBED PROBLEM FOR THE HYPERBOLIC EQUATION WITH INITIAL JUMP

In this paper we consider the initial-boundary value problem for a second order hyperbolic equation with initial jump. The bounds on the derivatives of the exact solution are given. Then a difference scheme is constructed on a non-uniform grid. Finally, uniform convergence of the difference solution is proved in the sense of the discrete energy norm.

THE APPLICATION OF INTEGRAL EQUATIONS TO THE NUMERICAL SOLUTION OF NONLINEAR SINGULAR PERTURBATION PROBLEMS

The nonlinear singular perturbation problem is solved numerically on nonequidistant meshes which are dense in the boundary layers. The method presented is based on the numerical solution of integral equations [1]. The fourth order uniform accuracy of the scheme is proved. A numerical experiment demonstrates the effectiveness of the method.