霍俊蓉1, 张荣培2
霍俊蓉, 张荣培. 求解极坐标系下反应扩散方程的紧致隐积分因子方法[J]. 数值计算与计算机应用, 2021, 42(2): 146-154.
Huo Junrong, Zhang Rongpei. COMPACT IMPLICIT INTEGRATION FACTOR METHOD FOR SOLVING REACTION DIFFUSION EQUATION IN POLAR COORDINATE[J]. Journal on Numerica Methods and Computer Applications, 2021, 42(2): 146-154.
Huo Junrong1, Zhang Rongpei2
MR(2010)主题分类:
分享此文:
[1] 张荣培, 王震, 王语, 韩子健. 反应扩散模型在图灵斑图中的应用及数值模[J]. 物理学报, 2018, 67(05): 51–59. [2] Tian C R. Turing Pattern Formation in a Semiarid Vegetation Model with Fractional-in-Space Diffusion[J]. Bull. Math. Biol., 2015, 77(11): 72–85. [3] Diego Alexander Garzón Alvarado. How the Formation of the Turing Pattern Could Be Used in a Bio-Mechano-Chemical Framework for Describing Development of Bones and Joints[J]. FASEB. J., 2019, 33(S1): 16.1. [4] Lacitignola D, Bozzini B, Frittelli M, Sgura I. Turing Pattern Formation on the Sphere for a Morphochemical Reaction-diffusion Model for Electrodeposition[J]. Commun. Nonlinear Sci. Numer. Simul., 2017, 48: 484–508. [5] Das D. Turing Pattern Formation in Anisotropic Medium[J]. J. Math. Chem., 2017, 55(3): 818– 831. [6] E. Özuǧurlu. A Note on the Numerical Approach for the Reaction-diffusion Problem to Model the Density of the Tumor Growth Dynamics[J]. Comput. Math. Appl., 2015, 69(12): 1504–1517. [7] Liu C, Li L, Wang Z, Wang R W. Pattern Transitions in a Vegetation System with Crossdiffusion[J]. Appl. Math. Comput., 2019, 342: 255–262. [8] Wang W M Liu H Y Cai Y L, Li Z Q. Turing Pattern Selection in a Reaction-diffusion Epidemic Model[J]. Chin. Phys. B., 2011, 20(07): 290–301. [9] Zhang R P, Wang Z, Liu J, Liu L M. A Compact Finite Difference Method for Reaction-diffusion Problems Using Compact Integration Factor Methods in High Spatial Dimensions[J]. Adv. Differ. Equ., 2018(1): 274. [10] Zhang R P, Yu X J, Zhu J, Abimael F D. Loula. Direct Discontinuous Galerkin Method for Nonlinear Reaction–diffusion Systems in Pattern Formation[J]. Elsevier Inc., 2014, 38(5–6): 1612– 1621. [11] 张荣培, 李明军, 蔚喜军.Chebyshev谱配置方法求解反应扩散方程组[J]. 数值计算与计算机应用, 2017, 38(4): 271–281. [12] Zhu, Y T, Zhang S, Newman A, Alber M. Application of Discontinuous Galerkin Methods for Reaction-diffusion Systems in Developmental Biology[J]. J. Sci. Comput., 2009, 40: 391–418. [13] Chen S Q, Zhang Y T. Krylov Implicit Integration Factor Methods For Spatial Discretization on High Dimensional Unstructured Meshes: Application to Discontinuous Galerkin Methods[J]. J. Comput. Phy., 2011, 230(11): 4336–4352. [14] Liu J, Tavener S. Semi-implicit Spectral Collocation Methods for Reaction-diffusion Equations on Annuli[J]. Numer. Methods Partial Diff. Equ., 2011, 27(5): 1113–1129. [15] 张荣培.求解反应扩散方程的紧致隐积分因子方法[J]. 中国海洋大学学报(自然科学版), 2012, 42(S1): 208–212. [16] Nie Q, Wan F, Zhang Y T, Liu X F. Compact Integration Factor Methods in High Spatial Dimensions[J]. J. Comput. Phy., 2008, 227(10): 5238–5255. [17] Gong Y Z, Wang Q, Wang Y S, Cai J X. A conservative Fourier Pseudo-spectral Method for the Nonlinear Schrödinger Equation[J]. J. Comput. Phy., 2017, 328: 354–370. [18] Schnakenberg J. Simple Chemical Reaction Systems with Limit Cycle Behaviour[J]. J. Theor. Biol., 1979, 81(3): 389–400. [19] Alber M, Glimm T, Hentschel H G E, Kazmierczak B, Zhang Y T, Zhu J F, Newman S A. The Morphostatic Limit for a Model of Skeletal Pattern Formation in the Vertebrate Limb[J]. Bull. Math. Biol., 2008, 70(2): 460–483. [20] Nie Q, Wan F Y M, Zhang Y T, et al. Compact Integration Factor Methods In High Spatial Dimensions[J]. J. Comput. Phy., 2008, 227(10): 5238–5255. |
[1] | 刘博, 陶善聪, 时晓天. 一种解抛物型方程的三层九点高精度加权差分格式[J]. 数值计算与计算机应用, 2022, 43(2): 163-175. |
[2] | 李辰, 郭启龙, 孙东, 刘朋欣. 一种求解双曲守恒律方程的中心型WENO格式[J]. 数值计算与计算机应用, 2020, 41(3): 246-258. |
[3] | 汪海鹭, 吴华. 二维非线性反应扩散方程的局部间断Galerkin谱元法[J]. 数值计算与计算机应用, 2020, 41(1): 1-18. |
[4] | 陈建灵, 冯仰德. 有限差分法求解声子热输运方程[J]. 数值计算与计算机应用, 2019, 40(3): 215-229. |
[5] | 尹旭, 卢朓, 姜海燕. 数值求解含时Wigner方程的一种高阶算法[J]. 数值计算与计算机应用, 2019, 40(1): 21-33. |
[6] | 张书华, 李景焕, 李瑜. PPP项目多阶段投资时机决策的最优多停时模型及数值求解[J]. 数值计算与计算机应用, 2018, 39(3): 205-216. |
[7] | 澈力木格, 何斯日古楞, 李宏. 大气污染模型的POD基降维有限差分算法[J]. 数值计算与计算机应用, 2018, 39(3): 172-182. |
[8] | 张荣培, 李明军, 蔚喜军. Chebyshev谱配置方法求解反应扩散方程组[J]. 数值计算与计算机应用, 2017, 38(4): 271-281. |
[9] | 邱俊, 胡晓, 王汉权. 数字图像修复的变分方法与实现过程[J]. 数值计算与计算机应用, 2016, 37(4): 273-286. |
[10] | 卿欢, 李晓, 纪光华, 张辉. 求解Cahn-Hilliard方程非线性项的两种数值格式对比[J]. 数值计算与计算机应用, 2016, 37(2): 95-115. |
[11] | 刘艳峰, 魏兵. 基于二维FDFD分析金属柱阵列的双站RCS[J]. 数值计算与计算机应用, 2014, 35(2): 81-91. |
[12] | 代健, 褚天舒, 杨照. 基于OpenCL的GPU加速三维时域有限差分电磁场仿真算法研究[J]. 数值计算与计算机应用, 2014, 35(1): 8-20. |
[13] | 吴正, 阳佳慧, 张依文. 具有巴黎期权特性的可转债定价问题研究[J]. 数值计算与计算机应用, 2013, 34(4): 295-304. |
[14] | 闵涛, 任菊成, 耿蓓. Chebyshev谱-Euler混合方法求解一类非线性Burgers方程[J]. 数值计算与计算机应用, 2013, 34(2): 81-88. |
[15] | 刘薇薇, 张亮, 马光克, 隋波, 张扬. TTI介质井间地震波场紧致交错网格高阶有限差分模拟及边界条件[J]. 数值计算与计算机应用, 2012, 33(4): 261-273. |
阅读次数 | ||||||
全文 |
|
|||||
摘要 |
|
|||||