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Implicit ODE solvers are not universally more robust than explicit ODE solvers

A very common adage in ODE solvers is that if you run into trouble with an explicit method, usually some explicit Runge-Kutta method like RK4, then you should try an implicit method. Implicit methods, because they are doing more work, solving an implicit system via a Newton method having “better” stability, should be…
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Sep 16, 2025Implicit ODE solvers are not universally more robust than explicit ODE solvers by cbolton11440

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