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Possible Duplicate:
Simplifying PDE

I have a pde:

$$u_{tt}-7u_{xx}-u_{x}=0$$

IC:

$$u(x,0) = x - x^2 $$ $$u_t(x,0) = 0$$

BC:

$$u(0,t) = 0 $$ $$u(L,t) = \sin(\pi t / 2)$$

$$t_\mathrm{last} = 2$$ $$L = 1$$

I was simplifying it using next formulas:

$$u(x,t)=e^{\lambda x + \mu t}\ V(x,t) $$ $$u_{x} = e^{\lambda x + \mu t}(\lambda V + V_{x})$$ $$u_{xx} = e^{\lambda x + \mu t}(\lambda^{2} V + 2\lambda V_{x} + V_{xx})$$ $$u_{tt} = e^{\lambda x + \mu t}(\mu^{2} V + 2\mu V_{t} + V_{tt})$$

After that I've got: $$V_{tt}-7V_{xx}-\frac{3}{28}V=0 $$ Help please: IC and BC must change, but how to change them? What will be new IC\BC?

  • 0
    A little. In this topic I've added results, which I've got.2011-12-26
  • 0
    The problem has just solved in previous topic. Thanks for Pacciu.2011-12-27

0 Answers 0