Thank you Roland for your reply!
In the meanwhile I was able to solve the issue. I changed my original
evolution requation
ζ̈=Aζ′+Bζ″+Cζ\ddot{\zeta} = A \zeta' + B \zeta'' +C \zeta into a system
(1) of
ζ˙=Π\dot{\zeta} = \PiΠ˙=Aζ′+Bζ″+Cζ\dot{\Pi}=A\zeta'+B\zeta''+C\zet I
wanted to avoid the second-order numerical derivatives by using a system (2)
ζ˙=Π\dot{\zeta}=\PiΠ˙=AH+BH′+Cζ\dot{\Pi}=AH+BH'+C\zetaH˙=Π′\dot{H}=\Pi'which
was source of the problem. This system is analytically equivalent to the
one above, but indeed not strongly hyperbolic.
I also had to change the boundaries near the r=0 region of the grid, but
the main issue was the aforementioned one. System (1) works with the new
boundary conditions.
Thank you very much!
Best regards,
Severin
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