Math 6610 • Analysis of Numerical Methods I

{Numerical PDEs} Consider the one-dimensional heat equation: Find
\(u(x,t)\) such that
\[
  u_t=u_{xx},\qquad t\geq0,\qquad x\in[0,1],\qquad
  u(x,0)=f(x),\qquad u(0,t)=u(1,t)=0.
\]
Describe how this problem might be solved by applying the Method of Lines and
Euler's Method. Give formulas that could be used to write a suitable computer
code.