摘要
为深入研究一维抛物方程的求解问题,利用Matlab软件使用Jacobi迭代法、Gauss–Seidel迭代法和两层网格算法对一维热传导抛物方程进行求解,分析不同算法的数值解与精确解.研究发现,在取得相同迭代误差的条件下,两层网格算法所需的迭代次数最少,且大大节省了运算时间,提高了运算的效率.
In order to deeply study the solution of one-dimensional parabolic equation, Jacobi iterative method, Gauss-Seidel iterative method and two-layer grid algorithm were used to solve one-dimensional heat conduction parabolic equation by Matlab software. The numerical and exact solutions of different algorithms were analyzed. It was found that under the condition of obtaining the same iteration error, the two-layer grid algorithm needs the least number of iterations. The operation time is greatly saved and the efficiency of operation is improved.
作者
李小珍
Li Xiaozhen(Anhui Vocational College of Defense Science and Technology)
出处
《哈尔滨师范大学自然科学学报》
CAS
2022年第6期18-21,46,共5页
Natural Science Journal of Harbin Normal University
基金
安徽省教学研究项目“课程思政视域下《高等数学》教学探索与实践”(2021jyxm0232)
关键词
抛物方程
网格算法
优越性
效率
Parabolic equation
Grid algorithm
Advantage
Efficiency
