Re: NDSolve

*To*: mathgroup at smc.vnet.net*Subject*: [mg65712] Re: NDSolve*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Sun, 16 Apr 2006 01:45:18 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*References*: <e1nnch$lnr$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Subbu wrote: > Hi, > > I have a question regarding usage of solution given by NDSolve function > > Suppose We have solved one ODE with NDSolve, it will give the solution > as interpolating function. Suppose I am solving a ODE for solution of y > as a function of x, I will get solution like > {y -> InterpolatingFunction[{{0., 1.}}, <>]}. > > Now I can get the values of y at any x using y[x]/.sol/.x->0.5 > > But Suppose I want to evaluate the y' [x](Derivative of y) how can we > get it that from the solution of NDSolve > > Thank you > Hi, Just use the prime symbol to get the value of the derivative at a given point. For example, In[1]:= eqns = {Derivative[1][y][x] == y[x] + Sin[x], y[0] == 2}; In[2]:= sol = NDSolve[eqns, y, {x, 0, 1}] Out[2]= {{y -> InterpolatingFunction[]}} In[3]:= y[x] /. sol /. x -> 0.5 Out[3]= {3.4432988011900783} In[4]:= Derivative[1][y][x] /. sol /. x -> 0.5 Out[4]= {3.9227506080049612} In[5]:= Plot[{y[x] /. sol, Derivative[1][y][x] /. sol}, {x, 0, 1}, PlotStyle -> {Blue, Red}]; Best regards, Jean-Marc