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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2014, Vol. 29 Issue (4): 375-388    DOI:
    
Legendre collocation method for the heat equation with nonlocal boundary conditions
YE Xing-de1, LIU Fei2, CHENG Xiao-liang1
1.Department of Mathematics, Zhejiang University, Hangzhou 310027, China
2. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
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Abstract  In this paper, Legendre collocation method for the heat equation with nonlocal boundary conditions is developed. The stability and convergence for its semidiscrete and fully discrete schemes are set up under some conditions. Numerical tests confirm these results.

Key words： Legendre collocation method      heat equations      nonlocal boundary condition     
Received: 21 May 2012      Published: 08 June 2018
CLC:  O241  
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YE Xing-de
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Cite this article:

YE Xing-de, LIU Fei, CHENG Xiao-liang. Legendre collocation method for the heat equation with nonlocal boundary conditions. Applied Mathematics A Journal of Chinese Universities, 2014, 29(4): 375-388.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2014/V29/I4/375


带非局部边界条件的热方程的LEGENDRE配置法

对带非局部边界条件的热方程的初边值问题提出了LEGENDRE配置法, 并给出其半离散逼近和全离散逼近的稳定性和收敛性分析. 数值试验验证了方法的有效性.

关键词： LEGENDRE配置法,  热方程,  非局部边界条件 
[1] LU Liang, GUO Xiu-feng. Existence of solutions for a nonlocal boundary value problem of fractional differential equations with $p$-Laplacian operator[J]. Applied Mathematics A Journal of Chinese Universities, 2015, 30(3): 262-270.