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Mathematica Calculus Equation Solving Wolfram Language

How to solve a higher order partial differential equation with boundaries

ihsan faseel

Posted 10 years ago

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POSTED BY: ihsan faseel

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Udo Krause

Udo Krause, NOrganization

Posted 9 years ago

Looks difficult, even setting all constants equal to 1 one gets In[8]:= DSolve[{D[y[x, t], {t, 2}] + D[y[x, t], {x, 4}] + D[y[x, t], {x, 4}, t] == 0, (y[x, t] /. x -> 0) == 0, (D[y[x, t], x] /. x -> 0) == 0, (D[y[x, t], {x, 2}] /. x -> L) == 0, (D[y[x, t], {x, 3}] /. x -> L) == 0}, y[x, t], {x, t}] Out[8]= (* actually the input ) so give L a value and try NDSolve: In[9]:= With[{L = 5}, NDSolve[{D[y[x, t], {t, 2}] + D[y[x, t], {x, 4}] + D[y[x, t], {x, 4}, t] == 0, (y[x, t] /. x -> 0) == 0, (D[y[x, t], x] /. x -> 0) == 0, (D[y[x, t], {x, 2}] /. x -> L) == 0, (D[y[x, t], {x, 3}] /. x -> L) == 0}, y[x, t], {x, t}] ] During evaluation of In[9]:= NDSolve::underdet: There are more dependent variables, {y[x,t],(y^(0,1))[x,t],(y^(0,2))[x,t]}, than equations, so the system is underdetermined. >> Out[9]= ( actually the input *) first job you should work on is to get a numerical solution with unit constants. Seemingly the problem is incorrect formulated.

Looks difficult, even setting all constants equal to 1 one gets

In[8]:= DSolve[{D[y[x, t], {t, 2}] + D[y[x, t], {x, 4}] + D[y[x, t], {x, 4}, t] == 0,
  (y[x, t] /. x -> 0) == 0, (D[y[x, t], x] /. x -> 0) == 0, (D[y[x, t], {x, 2}] /. x -> L) == 0, 
  (D[y[x, t], {x, 3}] /. x -> L) == 0}, y[x, t], {x, t}]
Out[8]= (* actually the input *)

so give L a value and try NDSolve:

In[9]:= With[{L = 5},
 NDSolve[{D[y[x, t], {t, 2}] + D[y[x, t], {x, 4}] + D[y[x, t], {x, 4}, t] == 0,
   (y[x, t] /. x -> 0) == 0, (D[y[x, t], x] /. x -> 0) == 0, (D[y[x, t], {x, 2}] /. x -> L) == 0, 
   (D[y[x, t], {x, 3}] /. x -> L) == 0}, y[x, t], {x, t}]
 ]

During evaluation of In[9]:= NDSolve::underdet: There are more dependent variables, {y[x,t],(y^(0,1))[x,t],(y^(0,2))[x,t]}, than equations, so the system is underdetermined. >>
Out[9]= (* actually the input *)

first job you should work on is to get a numerical solution with unit constants. Seemingly the problem is incorrect formulated.

POSTED BY: Udo Krause

ihsan faseel

Posted 10 years ago

sir, actually "E","I" ,"P","A","C" are constants. like : E-Youngs modulus. I-moment of inertia. A-area. C-damping coefficient. So what should i do sir.Should i define all these with there values.Actually i want to get a solution containing these constants as itself.