共查询到20条相似文献,搜索用时 31 毫秒
1.
A method of constructing an asymptotic solution of a singularly perturbed Volterra integral equation in the case of a spectral singularity of first order is proposed. 相似文献
2.
Numerical Algorithms - A singularly perturbed Volterra integro-differential equation with an integrable singularity in the integral term is considered. The upwind difference method is used to... 相似文献
3.
A. H. Khater A. B. Shamardan D. K. Callebaut M. R. A. Sakran 《Numerical Algorithms》2007,46(3):195-218
In this paper, a finite Legendre expansion is developed to solve singularly perturbed integral equations, first order integro-differential
equations of Volterra type arising in fluid dynamics and Volterra delay integro-differential equations. The error analysis
is derived. Numerical results and comparisons with other methods in literature are considered.
相似文献
4.
《Quaestiones Mathematicae》2013,36(2):229-248
Several investigations have been made on singularly perturbed integral equations. This paper aims at presenting an algorithm for the construction of asymptotic solutions and then provide a proof for asymptotic correctness to singularly perturbed systems of Volterra integro-differential equations. 相似文献
5.
M. Georgiou W. E. Olmstead 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1991,42(3):460-467
Certain singularly perturbed differential equations which exhibit boundary layer resonance are difficult to solve by the application of standard asymptotic methods. After reformulation as a singularly perturbed integral equation and treatment by a recently developed asymptotic methodology, the desired solution is obtained in a straightforward manner. 相似文献
6.
In this paper, we study a nonlinear first-order singularly perturbed Volterra integro-differential equation with delay. This equation is discretized by the backward Euler for
differential part and the composite numerical quadrature formula for integral part for which
both an a priori and an a posteriori error analysis in the maximum norm are derived. Based
on the a priori error bound and mesh equidistribution principle, we prove that there exists
a mesh gives optimal first order convergence which is robust with respect to the perturbation parameter. The a posteriori error bound is used to choose a suitable monitor function
and design a corresponding adaptive grid generation algorithm. Furthermore, we extend
our presented adaptive grid algorithm to a class of second-order nonlinear singularly perturbed delay differential equations. Numerical results are provided to demonstrate the
effectiveness of our presented monitor function. Meanwhile, it is shown that the standard arc-length monitor function is unsuitable for this type of singularly perturbed delay
differential equations with a turning point. 相似文献
7.
§ 1 . Introduction AclassofintegraldifferentialequationsDirichletboundaryvalueproblemsforordinarydif ferentialequationandellipticequationarediscussedin [1]and [2 ]respectively .Andin [3]akindofnonlocalproblemsforsingularlyperturbedreactiondiffusionsystemsarestudied.Inthispaper,whatisworthpointingoutisaclassofnonlinearboundaryvalueproblemsdiscussed,applyingthemethodofcompositeexpandandthetheoryofdifferentialinequalities.εy″ =f(x ,y ,Tεy ,ε) y′ +g(x ,y ,Tεy,ε) ,0 相似文献
8.
High-Accuracy Numerical Approximations to Several Singularly Perturbed Problems and Singular Integral Equations by Enriched Spectral Galerkin Methods 下载免费PDF全文
Sheng Chen 《数学研究》2020,53(2):143-158
Usual spectral methods are not effective for singularly perturbed problems
and singular integral equations due to the boundary layer functions or weakly singular solutions. To overcome this difficulty, the enriched spectral-Galerkin methods
(ESG) are applied to deal with a class of singularly perturbed problems and singular
integral equations for which the form of leading singular solutions can be determined.
In particular, for easily understanding the technique of ESG, the detail of the process
are provided in solving singularly perturbed problems. Ample numerical examples
verify the efficiency and accuracy of the enriched spectral Galerkin methods. 相似文献
9.
We consider the numerical discretization of singularly perturbed Volterra integro-differential equations (VIDE) (*) and Volterra integral equations (VIE) (**) by tension spline collocation methods in certain tension spline spaces, where is a small parameter satisfying 0<1, and q1, q2, g and K are functions sufficiently smooth on their domains to ensure that Eqs. (*) and (**) posses a unique solution.We give an analysis of the global convergence properties of a new tension spline collocation solution for 0<1 for singularly perturbed VIDE and VIE; thus, extending the existing theory for =1 to the singularly perturbed case. 相似文献
10.
奇摄动Volterra型积分微分方程Robin问题 总被引:11,自引:0,他引:11
本文利用上、下解证明了Volterra型积分微分方程解的存在性。然后,应用所获得的微分不等式理论,在适当的假设下,通过构造特殊的上、下解函数,证明Volterra型 奇摄动积分微分方程解的存在性,并给出一致有效的解的渐近估计。 相似文献
11.
N. N. Nefedov A. G. Nikitin T. A. Urazgil’dina 《Computational Mathematics and Mathematical Physics》2006,46(5):768-775
The Cauchy problem for a singularly perturbed Volterra integro-differential equation is examined. Two cases are considered: (1) the reduced equation has an isolated solution, and (2) the reduced equation has intersecting solutions (the so-called case of exchange of stabilities). An asymptotic expansion of the solution to the Cauchy problem is constructed by the method of boundary functions. The results are justified by using the asymptotic method of differential inequalities, which is extended to a new class of problems. 相似文献
12.
Linghai Zhang & Melissa Anne Stoner 《偏微分方程(英文版)》2012,25(4):295-329
The authors establish the existence and stability of standing wave solutions of a nonlinear singularly perturbed systemof integral differential equations and a nonlinear scalar integral differential equation. It will be shown that there exist six standing wave solutions (u(x,t),w(x,t))=(U(x),W(x)) to the nonlinear singularly perturbed system of integral differential equations. Similarly, there exist six standing wave solutions u(x,t)=U(x) to the nonlinear scalar integral differential equation. The main idea to establish the stability is to construct Evans functions corresponding to several associated eigenvalue problems. 相似文献
13.
Hermann Brunner 《计算数学(英文版)》1992,10(4):348-357
It is shown that the error corresponding to certain spline collocation approximations for nonlinear Volterra integral equations of the second kind is the solution of a nonlinearly perturbed linear Volterra integral equation. On the basis of this result it is possible to derive general estimates for the order of convergence of the spline solution at the underlying mesh points. Extensions of these techniques to other types of Volterra equations are indicated. 相似文献
14.
Gilberto Gonzalez Avalos Noe Barrera Gallegos 《Mathematical and Computer Modelling of Dynamical Systems: Methods, Tools and Applications in Engineering and Related Sciences》2013,19(5):483-503
A bond graph model for a singularly perturbed system is presented. This system is characterized by fast and slow dynamics. In addition, the bond graph can have storage elements with derivative and integral causality assignments for both dynamics. When the singular perturbation method is applied, the fast dynamic differential equation degenerates to an algebraic equation; the real roots of this equation can be determined by using another bond graph called singularly perturbed bond graph (SPBG). This SPBG has the characteristic that storage elements of the fast state and slow state have a derivative and integral causality assignment, respectively. Thus, a quasi-steady state model by using SPBG is obtained. A Lemma to get the junction structure from SPBG is proposed. Finally, the proposed methodology is applied to two examples. 相似文献
15.
Numerical Algorithms - In this paper, the numerical solution of a nonlinear first-order singularly perturbed differential equation with integral boundary condition is considered. The discrete... 相似文献
16.
R.Z. Khasminskii 《Journal of Differential Equations》2005,212(1):85-113
This work is concerned with diffusions with two-time scales or singularly perturbed diffusions. Asymptotic expansions of the solution of the associated Cauchy problem for parabolic partial differential equation are obtained and the desired error bounds are derived. These asymptotic expansions are then used to analyze related limit distributions of normalized integral functionals. 相似文献
17.
Carol Shubin 《Journal of Mathematical Analysis and Applications》2006,313(1):234-250
We study singularly perturbed Fredholm equations of the second kind. We give sufficient conditions for existence and uniqueness of solutions and describe the asymptotic behavior of the solutions. We examine the relationship between the solutions of the perturbed and unperturbed equations, exhibiting the degeneration of the boundary layer to delta functions. The results are applied to several examples including the Volterra equations. 相似文献
18.
研究了二阶非线性奇摄动微分方程的边值问题.利用匹配原则和微分不等式原理,得到一阶非线性问题的渐近解,进而得到二阶奇摄动问题的解的渐近估计. 相似文献
19.
We study functional differential equations with unbounded operator coefficients in Hilbert spaces such that the principal
part of the equation is an abstract hyperbolic equation perturbed by terms with delay and terms containing Volterra integral
operators. The well-posed solvability of initial boundary-value problems for the specified problems in weighted Sobolev spaces
on the positive semi-axis is established. 相似文献
20.
We analyze functional-differential equations with unbounded operator coefficients in a Hilbert space whose leading part is an abstract hyperbolic equation perturbed by terms with a retarded argument and by terms with Volterra integral operators.We consider spectral problems for the operator functions that are the symbols of abovementioned equations in the autonomous case. 相似文献