基于时空无网格法的两种算法求解电报方程  

Solve Telegraph Equations by Meshless Method in Space-Time

作　　者：朱妍红 宋灵宇[1] 盖梦琳 ZHU Yanhong;SONG Lingyu;GE Menglin(College of Science,Chang'an University,Xi'an 710064,China)

机构地区：[1]长安大学理学院,陕西西安710064

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2023年第5期512-520,共9页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学青年基金资助项目(12101482);中国博士后科学基金面上资助项目(2022M722604);陕西省科技厅重点研发一般资助项目(2023-YBSF-372)。

摘　　要：从时空距离的角度出发,分别用时空MQ径向基无网格法和时空MQ径向基耦合时空多项式基的无网格法在时空尺度框架下离散电报方程,将问题转化为求解线性方程组问题,求出电报方程的数值解,并比较两种方法的精度。然而大多数情况下,会造成系数矩阵本身是病态而无法求得稳定解,因此引入了奇异值分解技术求解线性方程组。数值实验结果表明:两种方法都可以得到逼近效果较好的数值解,耦合时空多项式基可以提高精度和稳定性,更适合用来数值计算。From the perspective of space-time distance,the space-time MQ radial basis meshless method and the space-time MQ radial basis coupled space-time polynomial-based meshless method are used to discretize the telegraph equation under the framework of space-time scale,and transform the problem into solving the linear equation system problem,the numerical solution of the telegraph equation is obtained,and also the accuracy of the two methods is compared in the paper.However,in most cases,the coefficient matrix itself is pathological and the stable solution of the equation is not able to be obtained,so the singular value decomposition technique is introduced to solve the system of linear equations.The numerical experimental results show that the numerical solution with good approximation effect is obtained by both methods,and the coupled space-time polynomial basis improves the accuracy and stability,which is more suitable for numerical calculation.

关 键 词：电报方程 时空径向基无网格法 时空径向基耦合时空多项式基无网格法 奇异值分解 

分 类 号：O241.82[理学—计算数学]