一类奇异抛物方程淬火解的数值分析  

Numerical Analysis of Quenching Solutions for a Class of Singular Parabolic Equations

作　　者：朱立平[1] 安家嘉 李智杰 ZHU Liping;AN Jiajia;LI Zhijie(Faculty of Science,Xi'an University of Architecture and Technology,Xi'an 710055,China)

机构地区：[1]西安建筑科技大学理学院,陕西西安710055

出　　处：《应用数学》2021年第4期950-957,共8页Mathematica Applicata

基　　金：国家自然科学基金(11702206)。

摘　　要：本文利用有限差分方法研究一类带奇异Neumann边界条件和奇异反应项的半线性抛物方程数值解的渐近行为.在初值满足一定假设的条件下,证明了数值解淬火速率与连续解淬火速率的一致性,数值淬火时间收敛于连续淬火时间,并通过数值实验验证了理论分析.In this paper, we study the asymptotic behavior of the numerical solution to a class of semilinear parabolic problem with singular Neumann boundary condition and singular reaction term by the finite difference method. Under some assumptions on the initial data, we prove that the numerical quenching rate is consistent with the continuous quenching rate and the numerical quenching time converges to the continuous one. Finally, we give some numerical experiments to verify the theoretical results.

关 键 词：奇异抛物方程 淬火率 有限差分 

分 类 号：O241.8[理学—计算数学]