Implicit-Explicit Runge-Kutta schemes for hyperbolic systems ... - utenti

We can consider the system of ode’s
Implicit-Explicit Runge Kutta schemes
y ′ = f(y) + 1
ε g(y),
where y = y(t) ∈ R N , f, g : R N → R N .
Splitting methods
A simple splitting consists in solving separately the non-stiff problem
y ′ = f(y),
applying an explicit scheme and, using an implicit scheme, the stiff problem
y ′ = 1
ε g(y).
Only first order accurate, but has several advantages:
⊲ Some properties of the solution are maintained (e.g. positivity, strong stability perserving
(SSP) property)
⊲ Consistency with the stiff limit as ε → 0
⊲ In many cases the implicit scheme for g can be explicitly solved
Remark Higher order splitting methods (ex. Strang splitting) can be constructed. Tipically
these extensions present a severe loss of accuracy when the g term is stiff.
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