Scientific Computing Lab Institut für Informatik Scientific Computing in Computer Science Scientific Computing Lab Partial Differential Equations Stationary Equations Dr. Miriam Mehl

Worksheet 2 – Solution a) Plot the function p(t) in a graph

Worksheet 2 – Solution b) Compute and plot approximate solutions with the help of explicit Euler and the method of Heun.

Worksheet 2 – Solution b) Compute and plot approximate solutions with the help of explicit Euler and the method of Heun.

Worksheet 2 – Solution d) Compute and plot approx. solutions with the help of implicit Euler and the Adams Moulton method.

Worksheet 2 – Solution d) Compute and plot approx. solutions with the help of implicit Euler and the Adams Moulton method.

Worksheet 2 – Solution d) Compute the approximation error for each case in b) and d).

Worksheet 2 – Solution d) Compute the approximation error for each case in b) and d).

Stationary Partial Differential Equations independent variables: space coordinates boundary value problems no start and end

Discretization functions operators finite difference/volume/element large system of linear equations typically sparse finite difference/volume/element

Iterative Solution of Systems of Linear Equations point-by-point processing eliminate local error iterate Gauss-Seidel solver

More Information http://www.cse.tum.de/vtc/SciComp/ 3.3 Discretizing partial Differential Equations 3.5 Iterative Solution of Large Sparse Linear Systems