i need to find analytical solution to these equations
- Thread starter richa
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HallsofIvy
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Rewrite the problem as \(\displaystyle \frac{\partial S}{\partial t}+ V_m= D\frac{\partial^2 S}{\partial x^2}\)
\(\displaystyle \frac{\partial (S+ V_mt)}{\partial t}= D\frac{\partial (S+ V_mt)}{\partial x^2}\).
Now let \(\displaystyle U= S+ V_m\) so the equation becomes \(\displaystyle \frac{\partial U}{\partial t}= D\frac{\partial^2U}{\partial x^2}\)
\(\displaystyle \frac{\partial (S+ V_mt)}{\partial t}= D\frac{\partial (S+ V_mt)}{\partial x^2}\).
Now let \(\displaystyle U= S+ V_m\) so the equation becomes \(\displaystyle \frac{\partial U}{\partial t}= D\frac{\partial^2U}{\partial x^2}\)