基于泛函修正平均法的第二类积分方程的改进迭代法
An Improved Iterative Method for the Second Kind of Integral Equation Based on Modified Functional Averaging Method
DOI: 10.12677/PM.2021.1110194, PDF,  被引量    国家自然科学基金支持
作者: 陈国林：西华师范大学数学与信息学院，四川 南充；陈 冲*：西华师范大学公共数学学院，四川 南充
关键词: 第二类积分方程；不动点；皮卡尔迭代；非线性；泛函修正平均法；The Second Kind of Integral Equation； Fixed Point； Picard Iteration； Nonlinear； Modified Functional Average Method
摘要: 本文将泛函修正平均法推广到第二类线性Volterra积分方程，并进行了误差分析。然后将该方法的第一次迭代进行了调整，即迭代求解u1过程中，对于非线性项中的un(t)采用含修正项的不完全代换u0n-1(t)(u0(t)+a1)形式。后将该方法应用到一类特殊形式的非线性Fredholm积分方程的求解中。最后通过算例验证了文中方法的可行性及有效性。
Abstract: In this paper, the modified functional average method is extended to the second kind of linear Volterra Integral Equation, and the error of the method is analyzed. Then the first iteration of the method is adjusted, that is, in the iterative solution of u1, the modified term which is in the in-complete substitution form of u0n-1(t)(u0(t)+a1) replaces the nonlinear term un(t). Then the method is applied to the solution of a special form of nonlinear Fredholm Integral Equation. Finally, the feasibility and effectiveness of the method are verified by numerical examples in this paper.
文章引用：陈国林, 陈冲. 基于泛函修正平均法的第二类积分方程的改进迭代法[J]. 理论数学, 2021, 11(10): 1728-1738. https://doi.org/10.12677/PM.2021.1110194

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