Re: Solving differential equations in Mathematica 7.0
- To: mathgroup at smc.vnet.net
- Subject: [mg108661] Re: Solving differential equations in Mathematica 7.0
- From: Wei-Li Tan <deathanubis at hotmail.com>
- Date: Fri, 26 Mar 2010 05:37:35 -0500 (EST)
- References: <hocm9d$shg$1@smc.vnet.net>
On 3=E6=9C=8824=E6=97=A5, =E4=B8=8B=E5=8D=885=E6=99=8233=E5=88=86, Wei-Li T=
an <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];P,L,disp are constant.
>
> and theMathematicareturn me the message:
>
> NDSolve::ndsz: At x ==x1, step size is effectively zero; singularity
> or stiff system suspected.
> FindRoot::cvmit: Failed to converge to the requested accuracy or
> precision within 100 iterations.
> NDSolve::berr: There are significant errors {xi} in the boundary
> value residuals.Returning the best solution found.
>
> {{z -> InterpolatingFunction[{{0.,25}}, <>], y ->
> InterpolatingFunction[{{0.,25}}, <>]}}
>
> How should I do to debug the code and find the correct solution.
> Any help on this matter will be greatly appreciated.
> Thanks
This is my code, when I use the smaller "disp"(like 0.001), the
program can be successfully implemented, but when I put "disp"
transfer large(like 0.02), the program will appear above error.
d = 0.61;
L = 25;
EIe = 6.022*10^4;
a = 10^-6;
b = 3;
Zy = 0.008;
P = 1000;
f1=EIe*(a-(a-1)*(((z[x]/Zy)^b)+1)^(-(b+1)/b));
f2=(EIe*(a-1)*(b+1)*((((z[x]/Zy)^b)+1)^(-2-(1/b)))
*((z[x]/Zy)^b))/z[x];
r=17.5;
Su = 40 ;
J = 0.5;
Pu = Min[(3 + r*x /Su + J* x/d)*Su*d, 9*Su*d];
Psoil = y[x]/(1/2956.5 + y[x]/Pu);
disp=0.02;
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]
Thank you for help.