restart: with(plots):
  H := a -> piecewise(a>=0,1):
  f1 := y->(H(y-1*Pi)-H(y-2*Pi))*sin(y)^2:

  g1:=(f1(y)/sqrt(4*Pi*t))*(sin((x-y)^2/4/t+Pi/4)-sin((x+y)^2/4/t+Pi/4)):
  g2:= int(g1, y= 0..100):

  g3:= diff(g2,t):
  g4:= diff(g2,x$2):
  g5:= (g3^2+g4^2)/2:
  E2:= unapply(Int(g5, x= 0..100, epsilon= 1e-4, digits= 7), t):
  CodeTools:-Usage( plot(E2, 0..20, numpoints= 50, labels= [t, E]));

The above mentioned code should give constant figure, but it takes a lot of time and not accurate.

If you can help me to improve these codes, I would be pleased.

Thanks!

I need a help about running the following codes..

restart:
d:=1:
s:=0.8:
c1:=sqrt((s)/Pi/r^3)/2 * (-sin(r*(u-1)^2/4/(s)+Pi/4)+sin(r*(u+1)^2/4/(s))/sqrt(2)):

c22:=-((u+1)/(4*Pi*r*sqrt(y-1)))*(exp(-r*y*(u+1)^2/(8*s)))*(sin(r*y*(u+1)^2/8/(s*(y-1))+Pi/4)/2+sin(r*y*(u-1)^2/8/(s*(y-1))+Pi/4)):
c2:=Int(c22, y= 1..100):

c33:=(sin(r*y*(u+1)^2/8/(s*(y-1))+Pi/4)+sin(r*y*(u-1)^2/8/(s*(y-1))+Pi/4))*(((d*s)/(Pi*(r^2)*y*sqrt(y-1))*exp(-r*y*(u+1)^2/8/s))-((d^2*sqrt((2*s^3)/(Pi*(y-1)*y^3*r^5)))*exp(d*(u+1)+(2*d^2*s)/(y*r))*erfc((r*y*(u+1)+4*d*s)/(2*sqrt(2*s*r*y))))):
c3:=Int(c33, y= 1..100):

g1:=c1+c2+c3:
g2:= unapply(Int(g1, r= 1..infinity, epsilon=1e-4,digits=7),u):
plot(g2, 0..10, numpoints=100);

Thank you!