If u(x, t) is the solution of \(\rm \frac{\partial u}{\partial t}=\frac{\partial^2 u}{\partial x^2}\), 0 < x < 1, t > 0
u(x, 0) = 1 + x + sin(π x) cos (πx)
u(0, t) = 1, u(1, t) = 2
then
1
\(\rm u\left(\frac{1}{2}, \frac{1}{4}\right)=\frac{3}{2}\)
2
\(\rm u\left(\frac{1}{2}, \frac{1}{2}\right)=\frac{3}{2}\)
3
\(\rm u\left(\frac{1}{4}, \frac{3}{4}\right)=\frac{5}{4}+\frac{1}{2} e^{-3 \pi^2}\)
4
\(\rm u\left(\frac{1}{4}, 1\right)=\frac{5}{4}+\frac{1}{2} e^{-4 \pi^2}\)