Re: Solving differential equations in Mathematica 7.0
- To: mathgroup at smc.vnet.net
- Subject: [mg108608] Re: Solving differential equations in Mathematica 7.0
- From: Narasimham <mathma18 at hotmail.com>
- Date: Thu, 25 Mar 2010 04:24:46 -0500 (EST)
- References: <hocm9d$shg$1@smc.vnet.net>
On Mar 24, 2:33 pm, Wei-Li Tan <deathanu... at hotmail.com> wrote:
> Hi,all:
> Here is the code I want to solve the equation
>
> Eqn1 := f2*(D[z[x], {x, 1}])^2 + f1*(D[z[x], {x, 2}]) + P*(D[y[x],
> {x, 2}]) + Psoil;
> Eqn2 := z[x] - (D[y[x], {x, 2}]);
>
> sol = NDSolve[{Eqn1 == 0, Eqn2 == 0, y[0] == disp, y'[0] == 0, y[L]
> == 0, y'[L] == 0}, {z, y}, {x, 0, L},
> MaxSteps -> Infinity, AccuracyGoal -> 10, StartingStepSize -> 0.001, MaxStepSize -> 0.005,
>
> MaxStepFraction -> 0.001]
>
> f1,f2 are the function of z[x]; Psoil is the function of y[x];
We should also specify how f1, f2 and Psoil depend on z[x] or y[x]
functionally and separately.
Since function of a function is involved, double underscoring notation
for functional dependence is necessary to be indicated. Like e.g.,
f1[z_[x_]] : = ( 2 - z[x] )/ ( x -2 )^2 ; Psoil[y_[x_]] : = y[x]
^2 ;
Narasimham