二维抛物型方程精细积分法与差分法比较

Comparison between Meticulous Integration and Difference Method for Solving Two-Dimensional Parabolic Equation

可用单内点子域精细积分法 ,求解二维抛物型方程初值问题 .当单内点精细积分中的传递函数即指数函数用 Taylor展开式的一阶近似来替代时 ,精细积分转化为差分方程 .研究这一对应关系 ,使各种常见差分格式均找到对应的单点精细积分格式 。

The initial-value problem of two-dimensional parabolic equation can be solved by using meticulous integration of single inner point subdomain. The meticulous integration is turned into difference equation in case transfer function, i.e. exponential function in meticulous integration of single inner point is replaced by Taylor expansion. This correspondence is studied, and each common difference scheme finds its corresponding meticulous integration of single point, and the unified expression is obtained in the general formula for meticulous integration of single point.