Newbie question, how to solve this simple ODE with ff++?

General Discussion
1

Hi guys,
I’m trying to solve this ODE

u''=6x
u(0)=0

with following script

/*
u''=6x
u(0)=0
*/
border b(i=0,1) {
  x=i;
  y=0;
}
meshL Sh=buildmeshL(b(50));
fespace Vh(Sh,P1);

Vh u,v;
func f = 6*x;
func real ue(int i) {
  if(i==0)
    return 0;
  return x;
}
int i=0;
func ue2 = ue(i++);

solve p(u,v,solver=CG)=int1d(Sh)(dx(u)*dx(v))-int1d(Sh)(f*v)+on(0,1,2,u=ue2);

plot(u,wait=true,value=true,fill=true);
for(int i=0;i<u[].n;i++) {
  cout << u[][i] << "\n";
}

I konw its analytic solution is x^3, but when I plot the numeric solution, I found they does not match. What’s wrong with my script? many thanks!

image
image965×476 12.5 KB

2

Hello, you can do as

/*
u''=6x
u(0)=0
u(1)=1
*/
border b(i=0,1) {
  x=i;
  y=0;
  label=i+1;
}
meshL Sh=buildmeshL(b(50));
fespace Vh(Sh,P1);

Vh u,v;
func f = -6*x;
// solve -u''=f

solve p(u,v,solver=CG)=int1d(Sh)(dx(u)*dx(v))-int1d(Sh)(f*v)+on(1,u=0.)+on(2,u=1.);

//plot(u,wait=true,value=true,fill=true);
//for(int i=0;i<u[].n;i++) {
//  cout << u[][i] << "\n";
//}
real error=sqrt(int1d(Sh)((u-x^3)^2));
cout << "error=" << error << endl;
3

Many thanks! I’ve learned a lot from your solution!