共查询到20条相似文献,搜索用时 0 毫秒
1.
Gennadi Vainikko 《Numerical Functional Analysis & Optimization》2013,34(3):313-338
We study the convergence and convergence speed of two versions of spline collocation methods on the uniform grids for linear Volterra integral equations of the second kind with noncompact operators. 相似文献
2.
Banach空间非线性脉冲Volterra积分方程组的整体解 总被引:1,自引:0,他引:1
研究Banach空间中定义在无穷区间R+上具有无穷多个脉冲点的非线性脉冲Volterra积分方程组解的存在性。给出了若干极值解的存在定理,改进了定义在有限区间上具有有限个脉冲点情形时该类方程的相应结果,并利用该结果讨论了一个无穷维积分方程组。 相似文献
3.
Constant-Sign Solutions for Systems of Fredholm and Volterra Integral Equations: The Singular Case 总被引:1,自引:0,他引:1
We consider the system of Fredholm integral equations
and also the system of Volterra integral equations
where T>0 is fixed and the nonlinearities h
i
(t,u
1,u
2,…,u
n
) can be singular at t=0 and u
j
=0 where j∈{1,2,…,n}. Criteria are offered for the existence of constant-sign solutions, i.e., θ
i
u
i
(t)≥0 for t∈[0,1] and 1≤i≤n, where θ
i
∈{1,−1} is fixed. We also include examples to illustrate the usefulness of the results obtained.
相似文献
4.
This article investigates backward stochastic Volterra integral equations in Hilbert spaces. The existence and uniqueness of their adapted solutions is reviewed. We establish the regularity of the adapted solutions to such equations by means of Malliavin calculus. For an application, we study an optimal control problem for a stochastic Volterra integral equation driven by a Hilbert space-valued fractional Brownian motion. A Pontryagin-type maximum principle is formulated for the problem and an example is presented. 相似文献
5.
Banach空间中非线性脉冲Volterra型积分方程组的可解性 总被引:2,自引:0,他引:2
张晓燕 《应用泛函分析学报》2004,6(1):65-72
在较弱的条件下,利用锥理论和单调迭代方法首先建立了Banach空间中一类非线性算子方程组最小最大解的存在性定理;然后作为应用,利用一个新的比较结果,得到了Banach空间中非线性脉冲Volterra型积分方程组的整体解,改进了最近的许多结果. 相似文献
6.
局部凸空间中一类非线性Volterra型积分方程解的存在性 总被引:3,自引:0,他引:3
首先利用局部凸空间非紧性测度得到一个新的不动点定理;并运用此定理研究了局部凸空间非线性V o lterra型积分方程解的存在性,然后应用到弱拓扑结构下对非线性V o lterra型积分方程解的存在性的讨论.推广了原有文献的结果. 相似文献
7.
Banach空间非线性脉冲Volterra型积分方程整体解的存在性定理及应用 总被引:7,自引:0,他引:7
利用一个新的比较结果和Monech不动点定理证明了Banach空间中非线性脉冲Volterra型积分方程整体解的存在性定理,并给出了对Banach空间中一阶脉冲微分方程初值问题的应用,改进了文(1-3)中的主要结果。 相似文献
8.
Spline Collocation-Interpolation Method for Linear and Nonlinear Cordial Volterra Integral Equations
Gennadi Vainikko 《Numerical Functional Analysis & Optimization》2013,34(1):83-109
We study the convergence and convergence speed of the discontinuous spline collocation and collocation-interpolation methods on uniform grids for linear and nonlinear Volterra integral equations of the second kind with noncompact operators. 相似文献
9.
The piecewise polynomial collocation method is discussed to solve linear Volterra integro-differential equations with weakly singular or other nonsmooth kernels. Using special graded grids, global convergence estimates are derived. The error analysis is based on certain regularity properties of the solution of the initial value problem.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
10.
Gennadi Vainikko 《Numerical Functional Analysis & Optimization》2013,34(12):1607-1637
We reduce a cordial Volterra integral equation of the first kind to a cordial integral equation of the second kind and establish a unique solvability of those in the scales of Banach spaces of C m -smooth functions on [0, T] and (0, T]. Stability estimates w.r.t. perturbation of data are derived. Polynomial and spline collocation methods are discussed for the solving the equation. 相似文献
11.
用边界元方法讨论了具有分片常系数电导率方程Δ↓(γΔ↓u)=0的Dirichlet边值问题,由于方程的基本解无法显式写出,在应用通常边界元时存在很大的困难,基于这个电导率方程的解的积分表达式,导出一个在边界和交界面上的积分方程组,并讨论了这个方程组的性质,对于这个积分方程组,用配点法进行求解,且给出其误差分析.相应的数值例子证实了算法的有效性.应该指出的是本文所用的方法也适用于具有分片常系数椭圆方程的不同边界问题。 相似文献
12.
本文考虑Banach 空间中形如x(t)= u(t)+ ∫Gtf(t,s,x(s))ds的广义Volterra 积分方程,通过引入一类偏序证明了所述方程相应的最大最小解的存在性. 相似文献
13.
Second-kind Volterra integral equations with weakly singular kernels typically have solutions which are nonsmooth near the initial point of the interval of integration. Using an adaptation of the analysis originally developed for nonlinear weakly singular Fredholm integral equations, we present a complete discussion of the optimal (global and local) order of convergence of piecewise polynomial collocation methods on graded grids for nonlinear Volterra integral equations with algebraic or logarithmic singularities in their kernels.
14.
15.
Gennadi Vainikko 《Numerical Functional Analysis & Optimization》2013,34(6):680-704
For (pure) cordial Volterra integral equations of the first kind, we establish stability estimates of the solution in the scales of Banach spaces of C m -smooth functions on (0, T] and on [0, T]. This enables to estimate the error of polynomial or generalized polynomial approximate solutions which are easy to be determined. 相似文献
16.
It is well known that, in contrast to Fredholm integral equations, iterated collocation solutions (based on collocation at the Gauss points) to Volterra integral equations of the second kind exhibit optimal discrete superconvergence only at the mesh points. Here, we show that some degree of global superconvergence is possible on the entire interval. 相似文献
17.
本文给出具分光滑边界Ω的域D包含C^n上的Cauchy-Fantappie型积分表示的内外极限值:Φ^ (t)=(1-β(t)/S)ψ(t) ∫Ω^ψ(ξ)K(ξ,t) Φ^-(t)=(-β(t)/S)ψ(t) ∫Ω^ψ(ξ)K(ξ,t)属于H(α,Ω),推广了陈叔谨先生1994年得到的一个结果。 相似文献
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19.
《Numerical Functional Analysis & Optimization》2013,34(2):249-269
ABSTRACT Fractional multistep methods were introduced by C. Lubich for the quadrature of Abel integral operators and the solution of weakly singular Volterra integral equations of the first kind with exactly given right-hand sides. In the current paper, we consider the regularizing properties of these methods to solve the mentioned integral equations of the first kind for perturbed right-hand sides. Finally, numerical results are presented. 相似文献
20.
Banach空间中不连续非线性Volterra型积分方程的唯一解 总被引:12,自引:0,他引:12
本文在一般序Banach空间中研究了不连续非线性Volterra型积分方程的唯一解.在非常弱的条件下证明了非线性Volterra型积分方程的唯一解可以由迭代序列的一致极限得到,并给出了逼近解的迭代序列的误差估计式,然后应用到一阶微分方程的初值问题,本质改进并推广了最近的一些结果. 相似文献