[Date Index]
[Thread Index]
[Author Index]
PDE with boundary condition ODE
*To*: mathgroup at smc.vnet.net
*Subject*: [mg50214] PDE with boundary condition ODE
*From*: mathma18 at hotmail.com (Narasimham G.L.)
*Date*: Sat, 21 Aug 2004 03:04:15 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
Beginning attempt to solve for z(x,y)(constant negative Gauss
curvature)in Monge form PDE r*t-s^2 == -(1+p^2+q^2)^2, with ODE BC as
p(x,0)^2=(1+z^2)/(2-z^2) for boundary y=0 has mixed lists. TIA for
help.
Clear[x,y,z,z2]; xm=.6; ym=3;
pde=-(1+D[z[x, y], x]^2+D[z[x, y], y]^2)^2 ==
(D[z[x, y],{x,2}]*D[z[x, y],{y,2}]-D[z[x, y],{x,y}]^2);
BC= {D[z[x, 0],x]^2 == (1+z[x,0]^2)/(2-z[x,0]^2),
z[0, 0]== .01,D[z[x,0],x]==.01};
"flat BC= {z[x,0]==x^2/5}" ;
NDSolve[{pde,BC},z,{x,0,xm},{y,0,ym}];
z2[u_,v_]=z[u,v]/.First[%];
Plot3D[z2[x,y],{x,0,xm},{y,0,ym}];
Prev by Date:
**GCD of a list of polynomial coefficient**
Next by Date:
**Re: Beware of adding 0.0**
Previous by thread:
**Re: GCD of a list of polynomial coefficient**
Next by thread:
**Do-loop conversion**
| |