Singular perturbation of general boundary value problem for higher-order elliptic equation containing two parameters

In this paper we consider the construction of asymptotic expression of solution for general boundary value problem for higher order elliptic equation containing two parameters. By using the method of two-parameter expression, asymptotic expression of solution and estimation corresponding to the remainder term are given. These results are the extensions of [1] and [7].     

Convergence of the approximate solution for the elliptic boundary value problem

The convergence of approximate solutions of boundary value problem of fourth order elliptic differential equations with uncontinuous coefficients in a rectangular region is investigated in this paper. This is useful for certain bending problems of rectangular plate on elastic supports.     

Asymptotic experssion of the solution of general boundary value problem for higher order elliptic equation with perturbation both in boundary and in operator

In this paper basing on (1) and (2), we study the singular perturbation of general boundary value problem for higher order elliptic equation with perturbation both in the boundary and in the operator, so as to establish the asymptotic expression involving two parameters. Thus, the iterative process of finding the asymptotic solution is derived and the estimation of the remainder term is given out, we extend and improve the previously published papers.     

Singular perturbation of general boundary value problem for higher order quasilinear elliptic equation involving many small parameters

In this paper applying M. I. Visik’s and L. R. Lyuster-nik’s^[1] asymptotic method and principle of fixed point of functional analysis, we study the singular perturbation of general boundary value problem for higher order quasilinear elliptic equation in the case of boundary perturbation combined with equation perturbation. We prove the existence and uniqueness of solution for perturbed problem. We give its asymptotic approximation and estimation of related remainder term.     

A Riemann-Hilbert boundary value problem in neutron transport theory

Summary A Riemann-Hilbert boundary value problem, occurring in neutron transport theory, is presented and solved in this note for the case of an infinite straight line and zero index.

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Sommario Viene presentato e risolto in questa nota un problema al contorno di Riemann-Hilbert di indice zero e relativo ad un intervallo infinito. Esso ha origine da un problema di diffusione di neutroni, studiato nell'ambito della teoria del trasporto.

     

Again discussing about singular perturbation of general boundary value problem for higher order elliptic equation containing two-parameter

In this paper using the method of The Two-Variable Expansion Procedure [11] we again discuss the construction of asymptotic expression of solution of general boundary value problem for higher order ellitptic equation containing two-parameter whose boundary condition is more general than [1]. We give asymptotic expression of solution as well as the estimation corresponding to the remainder term.     

The boundary layer scheme for a singularly perturbed problem for the second order elliptic equation in the rectangle

Using singularly perturbation theory is constructed the boundary layer scheme for a Dirichlet problem for the second order singularly perturbed equation of elliptic type in the rectangle. The error estimate is given.     

Singular perturbation of general boundary value problem for nonlinear differential equation system

I.IntroductionAllphysicalsystemsarenonlineartosomeextent.Actually,Lineal.systemisimaginarymodelwherenonlinearfactorisomittedinnonlinearsystem.Insolvingtheautocontl'ol,nonlinearoscillationtheory,theboundarystagnationproblenloffluidIncchanicsandsollleproblemsofsemi-conducttheoryandquantummechanicsetc'.weOnlyncedtosolvethefollowingproblem,whichisnonlineardifferentialequationsystemwithtilesll,allparanletel'inhighestorderderivativeandnonlinearboundaryconditions.whereE>0isasmallparameter,teR,x,fi…     

Interior layer behavior of boundary value problems for second order vector equation of elliptic type

In this paper, making use of the theory of partial differential inequalities, we will investigate the boundary value problems for a class of singularly perturbed second order vector elliptic equations, and obtain the existence and asymptotic estimation of solutions, involving the interior layer behavior, of the problems described above.     

二维双曲型方程初边值问题的块三对角并行求解算法

讨论用块三对角线性方程组的可扩展并行算法,求解带Dirichlet边界条件的一阶二维双曲型方程初边值问题。用本文方法在上海大学超级计算机自强3000上进行数值实验,实验结果与理论分析一致。在保证精度的前提下,得到线性加速比,并行效率达到90%以上。     

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 and prove that the solution of difference scheme in paper [1] uniformly converges to the solution of its original problem with order one.     

Singular perturbation of first boundary value problem for higher order elliptic equations (II)

In this paper we discuss singular perturbations of first boundary value problem for higher order elliptic equations of two parameter and obtain the asymptotic expression for the formal solution containing two-parameter as well as the estimation of its remainder term. These results are the extensions of (2) and (3).