一类非线性反应扩散方程的配置方法

Collocation methods for a nonlinear reaction-diffusion equation

对一类非线性反应扩散方程给出一种有限差分方法和配置法相结合的数值求解方法 .对建立的配置求解格式 ,不但证明了数值解的存在唯一性 ,并给出完整的数值分析 ,得到了最优的先验误差估计 .

Let a nonlinear reaction-diffusion PDE be solved approximately by a numerical method,which combines finite difference method and collocation method. The existence and uniqueness of the numerical solution of the scheme are proved. Numerical analysis and optimal order error estimate are derived.