变系数反应扩散方程的差分解法

A Compact Difference Method for the Variable Coefficient Reaction Diffusion Equations

研究了变系数反应扩散方程的差分格式.首先用Taylor公式导出紧差分格式;再通过补充边界值给出了此格式的求解形式;接着用能量方法证明了差分格式的解的存在性、唯一性、稳定性和收敛性;最后用数值例子验证了此方法的可行性和精确度.

A difference method for a variable coefficient reaction diffusion equation is studied.Firstly,a compact difference method is established using the Taylor formula.Secondly,by supplementing boundary values,the system of linear equations corresponding to the difference method becomes solved.Thirdly,by using the energy analysis method,the existence and uniqueness,the stability and convergence are all proved.Lastly,an example is given to show the feasibility and accuracy of the difference scheme.