摘要
常微分方程是解决实际问题的重要工具,生活中有很多具体问题的本质依赖于微分方程。然而理论研究中存在太多常微分方程无法求出解析解,这时利用数值方法求出其高精度解就显得格外重要。Picard迭代序列便是常微分方程定性理论中一类非常重要的迭代序列,以下将利用这种序列,结合龙贝格数值积分法对一类常微分方程进行数值求解,并用MATLAB进行传统方法的求解精度比对,从而凸显这种求解方法的重要地位。
Ordinary differential equation is an important tool to solve practical problems.However,there are too many ordinary differential equations in life to solve the analytical solution,so it is particularly important to use numerical method to solve its high-precision solution.Picard iterative sequence is a very important iterative sequence in the qualitative theory of ordinary differential equations.In this paper,we will use this sequence to solve a class of ordinary differential equations numerically combined with Romberg numerical integration method and compare the solution accuracy with MATLAB,so as to highlight the importance of this solution method.
作者
刘禹希
王密
LIU Yuxi;WANG Mi(College of Mathematics and Statistics,Wuhan University,Wuhan 430061,China;College of Remote Sensing Information Engineering,Wuhan University,Wuhan 430061,China)
出处
《佳木斯大学学报（自然科学版）》
CAS
2022年第4期161-163,170,共4页
Journal of Jiamusi University：Natural Science Edition
基金
2018年国家杰出青年科学基金项目(61825103)。
