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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Winter 2004 • Question 7

Question

Math 6610 • Analysis of Numerical Methods I Winter 2004 • Question 7

PDEs Consider the one-dimensional Heat Equation \[ u_t=u_{xx},\qquad t\ge 0,\qquad x\in [0,1],\qquad u(x,0)=f(x),\qquad u(0,t)=u(1,t)=0. \tag {11} \] Describe how to discretize this problem by applying the Method of Lines and the Backward Euler Method. Analyze the stability and local accuracy of your method.

Raw LaTeX

{PDEs}
Consider the one-dimensional Heat Equation
\[
  u_t=u_{xx},\qquad t\ge 0,\qquad x\in[0,1],\qquad
  u(x,0)=f(x),\qquad u(0,t)=u(1,t)=0. \tag{11}
\]
Describe how to discretize this problem by applying the Method of Lines and the
Backward Euler Method. Analyze the stability and local accuracy of your method.

Topic Tags

Absolute Stability and A-Stability Consistency, Stability, and Convergence Linear Programming and Optimization Von Neumann Stability Analysis