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。
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.
出处
《理论数学》
2021年第10期1728-1738,共11页
Pure Mathematics
