發(fā)布時(shí)間：2018-06-06 09:58

  本文選題：二維Fredholm型泛函積分方程 + 徑向基函數(shù)無網(wǎng)格解法��； 參考：《五邑大學(xué)》2017年碩士論文

【摘要】：本文利用徑向基函數(shù)無網(wǎng)格解法、最佳平方逼近解法、不動(dòng)點(diǎn)迭代與加速迭代解法等高效數(shù)值解法對(duì)二維Fredholm型泛函積分方程進(jìn)行求解,分別給出了數(shù)值算法格式、誤差估計(jì)和收斂性分析的結(jié)果,進(jìn)而給出數(shù)值例子闡明所提方法的可行性與可靠性.第一章主要給出了泛函積分方程解析解的存在唯一性定理及其適定性條件.第二章利用徑向基函數(shù)無網(wǎng)格解法對(duì)二維Fredholm型泛函積分方程進(jìn)行求解,并給出其數(shù)值算法格式、誤差估計(jì)和收斂性分析,進(jìn)而給出數(shù)值例子闡明了方法的可行性與可靠性.最佳平方逼近方法主要用于函數(shù)逼近問題,本文將此方法用于數(shù)值求解積分方程問題.第三章利用最佳平方逼近解法對(duì)二維Fredholm型泛函積分方程進(jìn)行求解,并給出其數(shù)值算法格式、誤差估計(jì)和收斂性分析,進(jìn)而給出數(shù)值例子闡明了方法的可行性與可靠性并與第二章所提方法進(jìn)行比較分析.不動(dòng)點(diǎn)迭代與加速迭代方法主要用于非線性方程的求根問題,本文將此方法運(yùn)用于數(shù)值求解泛函積分方程問題.第四章利用不動(dòng)點(diǎn)迭代,Aitken加速迭代及Steffensen加速迭代解法對(duì)二維Fredholm型泛函積分方程進(jìn)行求解,并給出其數(shù)值算法格式、誤差估計(jì)和收斂性分析,進(jìn)而給出數(shù)值例子闡明了方法的可行性與可靠性.
[Abstract]:In this paper, two dimensional Fredholm functional integral equations are solved by using the radial basis function meshless method, the best square approximation method, the fixed point iteration method and the accelerated iterative method. The results of error estimation and convergence analysis are given, and numerical examples are given to illustrate the feasibility and reliability of the proposed method. In chapter 1, we give the existence and uniqueness theorem of analytic solution of functional integral equation and the conditions of its fitness. In chapter 2, the radial basis function meshless method is used to solve the two-dimensional Fredholm functional integral equation, and its numerical algorithm format, error estimation and convergence analysis are given, and numerical examples are given to illustrate the feasibility and reliability of the method. The best square approximation method is mainly used in the function approximation problem. In this paper, the method is used to solve the integral equation numerically. In chapter 3, the optimal square approximation method is used to solve the two-dimensional Fredholm functional integral equation, and its numerical algorithm format, error estimation and convergence analysis are given. A numerical example is given to illustrate the feasibility and reliability of the method. The fixed point iterative and accelerated iterative methods are mainly used to find the root of nonlinear equations. This method is applied to solve the problem of functional integral equations numerically in this paper. In chapter 4, the fixed point accelerated iteration and Steffensen accelerated iterative method are used to solve the two-dimensional Fredholm functional integral equation. The numerical algorithm scheme, error estimation and convergence analysis are given. A numerical example is given to illustrate the feasibility and reliability of the method.
【學(xué)位授予單位】：五邑大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O241.83

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本文編號(hào)：1986126