杨雪花, 刘艳玲, 张海湘
杨雪花, 刘艳玲, 张海湘. 计算高维带弱奇异核发展型方程的交替方向隐式欧拉方法[J]. 计算数学, 2023, 45(1): 39-56.
Yang Xuehua, Liu Yanling, Zhang Haixiang. ALTERNATING DIRECTION IMPLICIT EULER METHOD FOR THE HIGH-DIMENSIONAL EVOLUTION EQUATIONS WITH WEAKLY SINGULAR KERNEL[J]. Mathematica Numerica Sinica, 2023, 45(1): 39-56.
Yang Xuehua, Liu Yanling, Zhang Haixiang
MR(2010)主题分类:
分享此文:
[1] Friedman A, Shinbrot M. Volterra integral equations in Banach space[J]. Transactions of the American Mathematical Society, 1967, 126(1):131-179. [2] Heard M L. An Abstract Parabolic Volterra Integrodifferential Equation[J]. SIAM Journal on Mathematical Analysis, 1982, 13(1):81-105. [3] López-Marcos J C. A difference scheme for a nonlinear partial integro-differential equation[J]. SIAM Journal on Numerical Analysis, 1990, 27(1):20-31. [4] Tang T. A finite difference scheme for a partial integro-differential equation with a weakly singular kernel[J]. Applied Numerical Mathematics, 1993, 11(4):309-319. [5] Yanik E G, Fairweather G. Finite element methods for parabolic and hyperbolic partial integrodifferential equations[J]. Nonlinear Analysis, 1988, 12(8):785-809. [6] Mustapha K, Mustapha H. A second-order accurate numerical method for a semilinear integrodifferential equation with a weakly singular kernel[J]. IMA Journal of Numerical Analysis, 2010, 30(2):555-578. [7] Chen H B, Xu D. A compact difference scheme for an evolution equation with a weakly singular kernel[J]. Numerical Mathematics-Theory, Methods and Applications, 2012, 5(4):559-572. [8] Chen H B, Xu D, Cao J L, Zhou J. A formally second order BDF ADI difference scheme for the three-dimensional time-fractional heat equation[J]. International Journal of Computer Mathematics, 2020, 97(5):1100-1117. [9] 张海湘, 杨雪花, 汤琼. 多项复合型黏弹性波问题的离散奇异卷积方法[J]. 湖南工业大学学报, 2019, 33(3):1-5. [10] 罗曼, 徐大, 吴珍珍. Crank-Nicolson/sinc方法求解带弱奇异核的偏积分微分方程[J]. 工业技术创新, 2020, 07(5):81-84. [11] 刘轩宇, 罗鲲, 王皓. 抛物型积分微分方程的新型全离散弱Galerkin有限元法[J]. 四川大学学报(自然科学版), 2020, 57(5):830-840. [12] 申雪, 王怡昕, 朱爱玲. 二阶线性抛物型积分微分方程的$(r, r-1, r-1)$ 阶弱Galerkin有限元数值模拟[J]. 山东师范大学学报(自然科学版), 2018, 33(3):271-277. [13] Hu S F, Qiu W L, Chen H B. A backward Euler difference scheme for the integro-differential equations with the multi-term kernels[J]. International Journal of Computer Mathematics, 2020, 97(6):1254-1267. [14] Qiu W L, Chen H B, Zheng X. An implicit difference scheme and algorithm implementation for the one-dimensional time-fractional Burgers equations[J]. Mathematics and Computers in Simulation, 2019, 166:298-314. [15] Peaceman D W, Rachford H H. The numerical solution of parabolic and elliptic differential equations[J]. Journal of the Society for industrial and Applied Mthematics, 1955, 3(1):28-41. [16] Cheng H, Lin P, Sheng Q, Tan R C E. Solving degenerate reaction-diffusion equations via variable step Peaceman-Rachford splitting[J]. SIAM Journal on Scientific Computing, 2004, 25(4):1273-1292. [17] Karaa S. A high-order compact ADI method for parabolic problems with variable coefficients[J]. Numerical Methods for Partial Differential Equations, 2006, 22:983-993. [18] 王文兵, 周辉, 马良, 程引会, 刘逸飞. 共形单步交替方向隐式时域有限差分方法及其改进[J]. 强激光与粒子束, 2018, 30(7):110-117. [19] 高林, 谢国大, 黄志祥, 许杰, 吴先良. 3维交替方向隐式时域有限差分算法及其应用[J]. 安徽大学学报(自然科学版), 2020, 44(4):52-59. [20] Zhang Y N, Sun Z Z. Alternating direction implicit schemes for the two-dimensional fractional sub-diffusion equation[J]. Journal of Computational Physics, 2011, 230(24):8713-8728. [21] Zhang Y N, Sun Z Z, Zhao X. Compact alternating direction implicit scheme for the twodimensional fractional diffusion-wave equation[J]. SIAM Journal on Numerical Analysis, 2012, 50:1535-1555. [22] Li L M, Xu D. Alternating direction implicit-Euler method for the two-dimensional fractional evolution equation[J]. Journal of Computational Physics, 2013, 236:157-168. [23] Lin Y P, Thomée V, Wahlbin L B. Ritz-Volterra projections to finite element spaces and applications to integro differential and related equations[J]. SIAM Journal on Numerical Analysis, 1991, 28:1047-1070. [24] McLean W, Thomée V. Numerical solution of an evolution equation with a positive-type memory term[J]. The ANZIAM Journal, 1993, 35(1):23-70. [25] Sloan I H, Thomée V. Time discretization of an integro-differential equation of parabolic type[J]. SIAM Journal on Numerical Analysis, 1986, 23(5):1052-1061. [26] Xu D. The global behavior of time discretization for an abstract Volterra equation in Hilbert space[J]. Calcolo, 1997, 34(1):93-116. |
[1] | 北京应用物理与计算数学研究所. 周毓麟先生在计算数学领域的成就与贡献——纪念周毓麟院士百年诞辰[J]. 计算数学, 2023, 45(1): 3-7. |
[2] | 付姚姚, 曹礼群. 矩阵形式二次修正Maxwell-Dirac系统的多尺度算法[J]. 计算数学, 2019, 41(4): 419-439. |
[3] | 王坤, 张扬, 郭瑞. Helmholtz方程有限差分方法概述[J]. 计算数学, 2018, 40(2): 171-190. |
[4] | 汤华中,邬华谟. 离散速度动力学方程组的数值方法研究 Ⅰ.半隐式差分格式[J]. 计算数学, 2000, 22(2): 183-190. |
阅读次数 | ||||||
全文 |
|
|||||
摘要 |
|
|||||