摘要
广义KPP(Kolmogorov-Petrovskii-Piskunov)方程是一个积分微分方程.为了要研究其数值解,我们首先将该方程转化为一个非线性双曲型方程,然后构造了一个线性化的差分格式.得到了差分格式解的存在唯一性.利用能量不等式证明了差分格式二阶收敛性和关于初值的无条件稳定性.数值结果验证了本文提出的方法.
The generalized KPP （Kolmogorov-Petrovskii-Piskunov） equation is an integro- differential equation. To investigate numerical solution for this problem, we first change the integro-differential equation to a form of nonlinear hyperbolic equation. Then a difference scheme is constructed to approximate initial boundary-value problem of hyperbolic equation. Existence and uniqueness are obtained for the difference scheme. Convergence and unconditional stability with respect to initial value are also discussed by using energy inequality. Numerical results illustrate the theoretical results of the presented method.
出处
《计算数学》
CSCD
北大核心
2009年第2期137-150,共14页
Mathematica Numerica Sinica
基金
国家自然科学基金(10871044)资助项目.
关键词
广义KPP方程
非线性双曲型方程
有限差分格式
收敛性
稳定性
generalized KPP equation
nonlinear hyperbolic equation
finite difference scheme
convergence, stability
