Math 6610 • Analysis of Numerical Methods I

Consider the initial-boundary-value problem
\[
  u=u(x,t)=?,\qquad u_t=u_{xx},\qquad x\in[0,1],\qquad t\geq0,
\]
subject to the initial and boundary conditions
\[
  u(x,0)=f(x),\qquad u(0,t)=g_0(t),\qquad u(1,t)=g_1(t)
\]
Explain how to use the method of lines to solve this problem. Describe the
scheme you obtain by using the Backward Euler Method to solve the resulting
ODEs and compute the local truncation error of that scheme.