Difference Schemes for the Nonlinear Equations in Partial Derivatives with Heredity

机译：具有遗传性的偏导数中非线性方程的差分格式

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We consider the initial-boundary value problem for nonlinear partial differential equations, the source of which are population models. Nonlinearity is contained both in the differential operator and in the inhomogeneity function. We construct a nonlinear implicit difference scheme, which requires the use of iterative solution methods on each time layer. Stability and convergence of the proposed numerical method were proved. Numerical experiments have been carried out, both on test examples and on the example of the biological model of the population.

机译：我们考虑非线性偏微分方程的初边值问题，其来源是种群模型。非线性包含在微分算子和不均匀函数中。我们构造了一个非线性隐式差分方案，该方案要求在每个时间层上使用迭代求解方法。证明了所提出数值方法的稳定性和收敛性。已经在测试实例和种群生物学模型的实例上进行了数值实验。

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来源
《Finite difference methods: theory and applications》|2018年|258-265|共8页
会议地点 Lozenetz(BG)
作者
T. V. Gorbova; V. G. Pimenov; S. I. Solodushkin;
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作者单位

Ural Federal University, Ekaterinburg, Russia;

Ural Federal University, Ekaterinburg, Russia,Institute of Mathematics and Mechanics, Ural Branch of the RAS, Ekaterinburg, Russia;

Ural Federal University, Ekaterinburg, Russia,Institute of Mathematics and Mechanics, Ural Branch of the RAS, Ekaterinburg, Russia;

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会议组织
原文格式 PDF
正文语种 eng
中图分类
关键词
Nonlinear difference scheme; Convergence of the difference scheme; Partial differential equation;

机译：非线性差分方案；差异方案的收敛；偏微分方程;

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专利

1. Numerical solving of partial differential equations with heredity and nonlinearity in the differential operator [J] . Gorbova T. V., Pimenov V. G., Solodushkin S. I. Sibirskie elektronnye matematicheskie izvestiia: Siberian Electronic Mathematical Reports . 2019,第23期

机译：在算子中具有遗传和非线性的偏微分方程的数值解。
2. Combined compact difference scheme for linear second-order partial differential equations with mixed derivative [J] . Spike T. Lee, Jun Liu, Hai-Wei Sun Journal of Computational and Applied Mathematics . 2014,第Null期

机译：带混合导数的线性二阶偏微分方程的组合紧致差分格式
3. Finite difference scheme for one system of nonlinear partial integro-differential equations [J] . Hecht Frederic, Jangveladze Temur, Kiguradze Zurab, Applied mathematics and computation . 2018,第期

机译：一个非线性部分积分微分方程一个系统的有限差分方案
4. Difference Schemes for the Nonlinear Equations in Partial Derivatives with Heredity [C] . T. V. Gorbova, V. G. Pimenov, S. I. Solodushkin International Conference on Finite Difference Methods . 2019

机译：具有遗传的部分衍生物非线性方程的差分方案
5. Three numerical schemes for solving nonlinear partial differential equations. [D] . Cheng, Kang-Ping. 2003

机译：求解非线性偏微分方程的三种数值格式。
6. Colloquium PaperNonlinear partial differential equations and applications: Some nonlinear elliptic equations from geometry [O] . YanYan Li 2007

机译：非线性偏微分方程及其应用：几何学中的一些非线性椭圆方程
7. High-order compact finite difference schemes for parabolic partial differential equations with mixed derivative terms and applications in computational finance [O] . Heuer Christof 2014

机译：具有混合导数项的抛物型偏微分方程的高阶紧致差分格式及其在计算金融中的应用
8. Analysis of Smoothing Operators in the Solution of Partial Differential Equations by Explicit Difference Schemes [R] . Vanderhouwen, P. J., Sommeijer, B. P., Wubs, F. W. 1986

机译：用显式差分格式分析偏微分方程解的平滑算子

Difference Schemes for the Nonlinear Equations in Partial Derivatives with Heredity

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