共查询到19条相似文献,搜索用时 55 毫秒
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解决了以混合偏导数优控的函数为核的第二类Fredholm积分方程类,当2≤p<∞, 相似文献
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核属于H函数类的多维积分方程近似解直接方法的优化 总被引:1,自引:1,他引:0
张新平 《数学的实践与认识》2001,31(4):447-452
本文我们确定了核属于 H函数类的多维第二类 Fredholm积分方程类在自适直接方法意义下的最优近似解的精确阶估计 ,并给出了最优算法 . 相似文献
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第一类弱奇异核Fredholm积分方程由于奇异及本质的不适定性,给求解带来很大难度.本文首先利用克雷斯变换将方程转化,并对转化后的方程进行高斯一勒让德离散,得到一离散不适定的线性方程组,结合正则化方法对该类问题进行数值求解.最后给出了数值模拟,验证了本文方法的可行性及有效性. 相似文献
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配置法是数值计算中常用的直接算法,具有数值稳定性好和计算精度高的优点.采用以hat函数为基底的配置法求解多维分数阶Fredholm积分方程.首先结合hat函数的性质,通过以hat函数为基底建立的配置法将分数阶积分方程转化为代数方程进行求解.然后在投影算子理论的框架下,建立了方程的收敛性理论并给出了误差分析.最后利用数值算例通过与其他数值方法相比较,验证了算法的高精度和高效率. 相似文献
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本文推广了Tikhonov正则化方法,导出了带复数核的第一类Fredholm积分方程的正则解应满足的正则积分微分方程,并讨论了正则解的收敛性·作为这一方法的应用,数值求解了与二维摇板造波问题相应的一类逆问题,并给出了选择最佳正则参数的一个实用的方法 相似文献
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球面上第二类Fredholm积分方程配置方法 总被引:1,自引:1,他引:0
胡国胜 《数学的实践与认识》2000,30(4)
球面上第二类 Fredholm积分方程经球坐标变换可化为矩形域 H0 上的问题求解 .用有限元法构造H0 上的插值函数 ,它必须满足在 H0 的左、右两边连续 ,然后用配置方程求方程的近似解 相似文献
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利用数值求积公式,将三维第一类Fredholm积分方程进行离散,通过引入正则化方法,将离散后的积分方程转化为一离散适定问题,通过广义极小残余算法得到了其数值解.数值模拟结果表明该方法的可行有效性. 相似文献
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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
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We consider the following system of Fredholm intergral equations u
i
(t)=0
1
g
i
(t,s)f
i
(s,u
1(s),u
2(s),...,u
n
(s)) ds, t[0,1], 1in. Criteria are offered for the existence of single, double and multiple solutions of the system that are of constant signs. The generality of the results obtained is illustrated through applications to several well known boundary value problems. We also extend the above system of Fredholm intergral equations to that on the half-line [0,) u
i
(t)=0
g
i
(t,s)f
i
(s,u
1(s),u
2(s),...,u
n
(s)) ds, t[0,), 1in and investigate the existence of constant-sign solutions. 相似文献
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The exact order of ε-complexity is determined in L
p
(2 ≤p < ∞) spaces for the second kind of Fredholm integral equations with kernels belonging to an isotropic Sobolev class.
Received December 10, 1999, Accepted April 19, 2002 相似文献
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Ravi P. Agarwal Donal O'Regan Patricia J. Y. Wong 《Mathematical Methods in the Applied Sciences》2010,33(15):1783-1793
We consider the system of Fredholm integral equations where T>0 is fixed and the nonlinearities Hi(t, u1, u2, …, un) can be singular at t=0 and uj=0 where j∈{1, 2, …, n}. Criteria are offered for the existence of constant‐sign solutions, i.e. θiui(t)≥0 for t∈[0, 1] and 1≤i≤n, where θi∈{1,?1} is fixed. We also include an example to illustrate the usefulness of the results obtained. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
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In this paper numerical solution of system of linear Fredholm integral equations by means of the Sinc-collocation method is considered. This approximation reduces the system of integral equations to an explicit system of algebraic equations. The exponential convergence rate of the method is proved. The method is applied to a few test examples with continuous kernels to illustrate the accuracy and the implementation of the method. 相似文献
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<正>The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented.Existence and uniqueness of optimal solutions is proved. A collective Gauss-Seidel scheme and a multigrid scheme are discussed.Optimal computational performance of these iterative schemes is proved by local Fourier analysis and demonstrated by results of numerical experiments. 相似文献
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In this paper, we suggest a method for solving Fredholm integral equation of the first kind based on wavelet basis. The continuous Legendre and Chebyshev wavelets of the first, second, third and fourth kind on [0,1] are used and are utilized as a basis in Galerkin method to approximate the solution of integral equations. Then, in some examples the mentioned wavelets are compared with each other. 相似文献