Take the 2-minute tour ×
Mathematica Stack Exchange is a question and answer site for users of Mathematica. It's 100% free, no registration required.

NDSolve::ivone: Boundary values may only be specified for one independent variable. Initial values may only be specified at one value of the other independent variable. >>

I keep getting this, although I wish to use NDSolveValue to solve the following differential equation: $\ u_{xx}-\frac{u_t}{\sqrt{t^2+x^2}}=-6u^5+(8+4e)u^3-(2+4e)u $ where e is a parameter, with the initial conditions being $\ u(0.001,x)=tanh(x), u_t(0.001,x)=0$ and the boundary conditions being $\ u(t,0)=0,u(t,6)=1 $. I have loads of operations I wish to perform on the solution, but every single operation depends on getting the solution in the first place. Here's the code I intend to run in order to perform everything I want on it:

eps4 = 0;
phi6m4 = NDSolveValue[{
   D[u[t, x], x, x] - 
   D[u[t, x], t]*1/Sqrt[t^2 + x^2] == -6 u[t, x]^5 +
         (8 + 4 eps4) u[t, x]^3 - (2 + 4 eps4)u[t, x],
   u[0.001, x] == Tanh[x],
   Derivative[1, 0][u][0.001, x] == 0,
   u[t, 0] == 0, u[t, 7] == 1}
     , u, {t, 0.001, 6}, {x, 0, 7}];

NDSolveValue::ivone: Boundary values may only be specified for one independent variable. Initial values may only be specified at one value of the other independent variable. >>

share|improve this question
1  
the error is in NDSolveValue, why post all that other stuff? –  george2079 Mar 5 at 20:19
1  
The error arises due to specifying initial condition on both u and D[u,t] which is not permissable since the system is first order in t. –  george2079 Mar 5 at 20:29
add comment

1 Answer 1

As it is already mentioned in the comments, the initial condition Derivative[1, 0][u][0.001, x] == 0, should not appear there. After it removal the equation is solved as expected:

    eps4 = 0;
phi6m4V = 
 NDSolveValue[{D[u[t, x], x, x] - 
     D[u[t, x], t]/
      Sqrt[t^2 + x^2] == -6 u[t, x]^5 + (8 + 4 eps4) u[t, x]^3 - (2 + 
        4 eps4) u[t, x], u[0.001, x] == Tanh[x], u[t, 0] == 0, 
   u[t, 7] == 1}, u, {t, 0.001, 6}, {x, 0, 7}]

This

 Plot3D[phi6m4V[t, x], {t, 0.001, 6}, {x, 0, 7}]

Shows the solution: enter image description here

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.