请教大家,关于龙格库塔法

femainder

计算流中用到的龙格库塔法和数值分析书中讲的一般的龙格库塔法一样吗
数值分析书上讲的是用龙格库塔法解常微分方程的初值问题,和计算流中常用的龙格库塔法是一回事吗
如果想了解计算流中的龙格库塔法看一些什么材料,非常感谢!!

shunliu

the idea is the same. for instance, the eqn has the following form: du/dt+u*du/dx=0. this is a pde. it can be rewritten as:du/dt=-u*du/dx.
the rhs can be calculated by empploying, say, Central Differece. Now that you know the values of the rhs at every interior points, you can apply the R-K scheme to the above eqn just as for ode.