Scientific Computing Lab

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Scientific Computing Lab
Scientific Computing in Computer Science
Institut für Informatik

• Partial Differential Equations
• Stationary Equations

Dr. Miriam Mehl
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Worksheet 2 Solution
a) Plot the function p(t) in a graph
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Worksheet 2 Solution
b) Compute and plot approximate solutions with
the help of explicit Euler and the method of
Heun.
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Worksheet 2 Solution
b) Compute and plot approximate solutions with
the help of explicit Euler and the method of
Heun.
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Worksheet 2 Solution
d) Compute and plot approx. solutions with the
help of implicit Euler and the Adams Moulton
method.
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Worksheet 2 Solution
d) Compute and plot approx. solutions with the
help of implicit Euler and the Adams Moulton
method.
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Worksheet 2 Solution
d) Compute the approximation error for each case
in b) and d).
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Worksheet 2 Solution
d) Compute the approximation error for each case
in b) and d).
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Stationary Partial Differential Equations

• independent variables space coordinates
• boundary value problems
• no start and end

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Discretization

• functions
• operators
• large system of linear equations
• typically sparse

finite difference/volume/element
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Iterative Solution of Systems of Linear Equations

• point-by-point processing
• eliminate local error
• iterate
• Gauss-Seidel solver

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More Information

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