ux(x,t)+k[tanh(x)]ut(x,t)=0;
u(x,0)=u0(x);
I solved the equation by the method of characteristics and found x(t)=sinh-1(ektsinhx0) and so the solution is u(x,t)=u0{sinh-1[e-ktsihnx]}.
Now my real hustle is the following
(Typed exactly as the lecturer asked it):
What you really want to see is how a ‘solitary’ initial state such as
u0(x)={ a0x2(1-x)2 for 0<=x<=1
{ 0 for x>1
will deform as time goes on.Remember that it will not deform at all if c is constant.
Do this by well-known methods and produce some video frames. You will have to
perform some elementary numerical calculations for which the code should be set
out in an appendix.
Please help me,
u(x,0)=u0(x);
I solved the equation by the method of characteristics and found x(t)=sinh-1(ektsinhx0) and so the solution is u(x,t)=u0{sinh-1[e-ktsihnx]}.
Now my real hustle is the following
(Typed exactly as the lecturer asked it):What you really want to see is how a ‘solitary’ initial state such as
u0(x)={ a0x2(1-x)2 for 0<=x<=1
{ 0 for x>1
will deform as time goes on.Remember that it will not deform at all if c is constant.
Do this by well-known methods and produce some video frames. You will have to
perform some elementary numerical calculations for which the code should be set
out in an appendix.
Please help me,
