A second order uniform difference scheme for a singularly perturbed turning point problem

We construct a positive type difference scheme.for a singularly perturbed boundary value problem with a turning point. It's proved that this scheme is the second order convergence, uniformly in ε, to the solution of the singularly perturbed B.V.P. Numerical examples are provided.     

A uniform high-order method for a singular perturbation problem in conservative form

A uniform high order method is presented for the numerical solution of a singular perturbation problem in conservative form. We firest replace the original second-order problem (1.1) by two equivalent first-order problems (1.4), i.e., the solution of (1.1) is a linear combination of the solutions of (1.4). Then we derive a uniformly O(h~m+1)accurate scheme for the first-order problems (1.4), where m is an arbitrary nonnegative integer, so we can get a uniformly O(h~m+1) accurate solution of the original problem (1.1) by relation (1.3). Some illustrative numerical results are also given.     

求解奇异摄动转向点问题的高精度方法

1.引言 本文考察以下奇异摄动转向点问题: Lu≡ε~2u″+xa(x)u′-b(x)u=f(x),x∈I=[-1,1], u(-1)=A,u(1)=B, (1.1)其中参数ε是(0,1]中的常数,函数a(x)∈C~3[I],b(x),f(x)∈C~4[I]且满足a(x)≥a_*>0,b(x)≥b_*>0.在以上假设下,由[1]知,方程(1.1)存在唯一解u_8∈C~5[I]且     

在非均匀网格上解椭圆—双曲型偏微分方程奇异摄动问题

本文考察了椭圆一双曲型偏微分方程奇异摄动问题(1.1),证明了迎风差分格式在一特殊的非均匀网格上是一阶一致收敛的.最后给出了一些数值结果.     

Numerical solution of a singularly perturbed elliptichyperbolic partial differential equation on a nonuniform discretization mesh

In this paper, we consider the upwind difference scheme for singular perturbation problem (1.1). On a special discretization mesh, it is proved that the solution of the upwind difference scheme is first order convergent, uniformly in the small parameter ε, to the solution of problem (1.1). Numerical results are finally provided.     

求解奇异摄动转向点问题的一个高阶格式

§1.引言本文考虑以下奇异摄转向点问题: (1.1)这里参数ε是(0,1]中常数,函数α(x)∈C~2[I],b(x),f(x)∈C~3[I],且满足α(x)≥α_*>0,b(x)≥b_*>0,在以上假设下,由[2]可知,方程(1.1)存在唯一解u_ε∈C~4[I],且满足以下不等式     

A coupling difference scheme for the numerical solution of a singular perturbation problem

In this paper, we consider a singularly perturbed problem without turning points. On a special diseretization mesh, a coupling difference scheme, resulting from central difference scheme and Abrahamsson-Keller-Kreiss box scheme, is proposed and the second order convergence, uniform in the small parameter, is proved. Finally, numerical resulls are provided.     

求解奇异摄动问题的一个耦合差分格式

本文考察奇异摄动问题(1.1).在一特殊的非均匀网格上,将不稳定、二阶精度的中心差格式和稳定、一阶精度的Abrahamsson-Keller-Kreiss箱子格式相耦合,得到了一个二阶一致收敛的差分格式.最后给出了数值结果.     

求解奇异摄动转向点问题的一个二阶一致收敛格式

本文对奇异摄动转向点问题构造了一个关于ε一致收敛的二阶正型格式,并给出了数值例子.