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研究了一类非线性奇摄动方程的激波问题.利用Sinc-Galerkin方法,构造出边值问题的激波解,并由Newton法得到其近似解.
关键词:
非线性方程
激波
Sinc-Galerkin方法
Newton法 相似文献
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Asymptopic solution for a class of semilinear singularly perturbed fractional differential equation 下载免费PDF全文
This paper considers a class of boundary value problems for the semilinear singularly perturbed fractional differential equation.Under the suitable conditions,first,the outer solution of the original problem is obtained;secondly,using the stretched variable and the composing expansion method the boundary layer is constructed;finally,using the theory of differential inequalities the asymptotic behaviour of solution for the problem is studied and the uniformly valid asymptotic estimation is discussed. 相似文献
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A singularly perturbed periodic in time problem for a parabolic reaction-diffusion equation in a two-dimensional domain is studied. The case of existence of an internal transition layer under the conditions of balanced and unbalanced rapid reaction is considered. An asymptotic expansion of a solution is constructed. To justify the asymptotic expansion thus constructed, the asymptotic method of differential inequalities is used. The Lyapunov asymptotic stability of a periodic solution is investigated. 相似文献
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A sequence converging to the solution of the Cauchy problem for a singularly perturbed weakly nonlinear first-order differential equation is constructed. This sequence is asymptotic in the sense that the distance (with respect to the norm of the space of continuous functions) between its nth element and the solution to the problem is proportional to the (n + 1)th power of the perturbation parameter. Such a sequence can be used to justify asymptotics obtained by the boundary function method. 相似文献
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D. D. Bainov M. A. Hekimova V. M. Veliov 《International Journal of Theoretical Physics》1989,28(2):209-225
A justification is given of an asymptotic method for solving a boundary value problem for a linear singularly perturbed impulsive system of differential equations with fast and slow variables. 相似文献
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A singularly perturbed reaction diffusion problem forthe nonlinear boundary condition with two parameters 下载免费PDF全文
A class of singularly perturbed initial boundary value
problems of reaction diffusion equations for the nonlinear boundary
condition with two parameters is considered. Under suitable
conditions, by using the theory of differential inequalities, the
existence and the asymptotic behaviour of the solution for the initial boundary
value problem are studied. The obtained solution indicates that
there are initial and boundary layers and the thickness of the
boundary layer is less than the thickness of the initial layer. 相似文献
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The solution of a singularly perturbed differential equation is considered that describes the passage of a steady current in a system consisting of a mixture of charged particles. A correction to the solution is obtained by splicing two asymptotic solutions. Proceeding from the magnitude of this correction, the region of applicability of this method is determined. 相似文献
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Error Analysis for a Non-Monotone FEM for a Singularly Perturbed Problem with Two Small Parameters 下载免费PDF全文
Yanping Chen Haitao Leng & Li-Bin Liu 《advances in applied mathematics and mechanics.》2015,7(2):196-206
In this paper, we consider a singularly perturbed convection-diffusion problem.
The problem involves two small parameters that gives rise to two boundary layers
at two endpoints of the domain. For this problem, a non-monotone finite element
methods is used. A priori error bound in the maximum norm is obtained. Based on
the a priori error bound, we show that there exists Bakhvalov-type mesh that gives
optimal error bound of$\mathcal{O}(N^{−2})$ which is robust with respect to the two perturbation
parameters. Numerical results are given that confirm the theoretical result. 相似文献