A UNIFORMLY DIFFERENCE SCHEME OF SINGULAR PERTURBATION PROBLEM FOR A SEMILINEAR ORDINARY DIFFERENTIAL EQUATION WITH MIXED BOUNDARY VALUE CONDITION

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THE UNIFORMLY CONVERGENT DIFFERENCE SCHEMES FOR A SINGULAR PERTURBATION PROBLEM OF A SELFADJOINT ORDINARY DIFFERENTIAL EQUATION

In this paper,we construct a class of difference schemes with fitted factors for asingular perturbation problem of a self-adjoint ordinary differential equation.Using adifferent method from[1],by analyzing the truncation errors of schemes,we give thesufficient conditions under which the solution of the difference scheme converges uniformlyto the solution of the differential equation.From this we propose several specific schemesunder weaker conditions,and give much higher order of uniform convergence,and applyingthem to example,obtain the numerical results.     

A SINGULAR PERTURBATION PROBLEM FOR PERIODIC BOUNDARY DIFFERENTIAL EQUATION

In this paper, we consider a second order ordinary differential equation with a small,positive parameter ε in its highest derivative for periodic boundary values problem andprove that the solution of difference scheme in paper [1] uniformly converges to the solutionof its original problem with order one.     

奇异摄动偏微分方程的周期边界问题

本文讨论奇异摄动椭圆抛物型偏微分方程的周期边界问题.构造一个差分格式,利用分离解的奇性项的方法,结合问题的渐近展开,证明所构造的差分格式具有O(τ h~2)一致收敛阶.     

A UNIFORMLY CONVERGENT SECOND ORDER DIFFERENCE SCHEME FOR A SINGULARLY PERTURBED SELF-ADJOINT ORDINARY DIFFERENTIAL EQUATION IN CONSERVATION FORM

In this paper,based on the idea of El-Mistikawy and Werle[1]we construct a differencescheme for a singularly perturbed self-adjoint ordinary differential equation inconservation form.We prove that it is a uniformly convergent second order scheme.     

Jacobi和Gauss-Seidel迭代收敛的新判别准则

设线代数方程组 Ax=bA=D-E-F,其中D、E、F分别为A的对角、严格下三角、严格上三角矩阵。此时Jacobi迭代阵和Gauss—Seidel迭代阵分别为 B=D~(-1)(E+F)=L+U, B’=(D-E)~(-1) F=(I-L)~(-1)U     

解含有混合导数项的抛物型方程的一个显格式

考虑含有混合导数项的三维抛物型方程第一边值问题: 0相似文献   

A class of three-level explicit schemes with higher stability properties for a dispersive equation ut=auxxx

In this paper, a class of three level explicit schemes for a dispersive equation u_t=au_xxx with stability condition |r|=|α|Δt/(Δx)³≤2.382484, are considered. The stability condition for this class of schemes is much better than |r|≤0.3849 in [1], [2] and |r|≤0.701659 in [3], and |r|≤1.1851 in [4].     

A uniformly convergent second order difference scheme for a singularly perturbed self-adjoint ordinary differential equation in conservation form

In this paper, based on the idea of El-Mistikawy and Werle⁽¹⁾ we construct a difference scheme for a singularly perturbed self-adjoint ordinary differential equation in conservation form. We prove that it is a uniformly convergent second order scheme.     

Bending of corner-supported rectangular plate under concentrated load

In this paper the solution for the bending of corner-supported rectangular plate under concentrated load at any point (α/2, η) of the middle line of the plate is given by means of a conception called modified simply supported edges and the method of superposition. Some numerical example is presented. The solution obtained by this method checks very nicely with what was obtained by G.T. Shih^[3] by means of spline finite element method when η=d/2. This shows that this method of solution is satisfactory.