Heat-wave lets you solve heat and wave sheets with three methods: forward-difference, backward-difference,
and central-difference.
With backward-difference you can take choose very big time steps.
You loose accuracy, but you can quickly get an approximate solution.
However, with forward-difference choosing a large time step results in an unstable and non-converging solution.
All of the illustrations on this page were generated by solving the heat equation with rates greater than one half.
1D, rate 1/2 is stable but oscillates.
Equation.
Greater than 0.5 in unstable.
1/2 overshoots.
1/3 works fine.
1/4 looks like an attractive distribution.
2D case max rate is 0.25.
Even backward difference blows up with negative values.
Central difference.
Slicing.
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Heat-wave lets you solve heat and wave sheets with three methods: forward-difference, backward-difference,
and central-difference.
With backward-difference you can take choose very big time steps.
You loose accuracy, but you can quickly get an approximate solution.
However, with forward-difference choosing a large time step results in an unstable and non-converging solution.
1D, rate 1/2 is stable but oscillates.
Equation.
Greater than 0.5 in unstable.
1/2 overshoots.
1/3 works fine.
1/4 looks like an attractive distribution.
2D case max rate is 0.25.
Even backward difference blows up with negative values.
Central difference.
Slicing.