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A posteriori error estimation for multi-stage Runge-Kutta IMEX schemes. (English) Zbl 1365.65183

Summary: Implicit-explicit (IMEX) schemes are widely used for time integration methods for approximating solutions to a large class of problems. In this work, we develop accurate a posteriori error estimates of a quantity-of-interest for approximations obtained from multi-stage IMEX schemes. This is done by first defining a finite element method that is nodally equivalent to an IMEX scheme, then using typical methods for adjoint-based error estimation. The use of a nodally equivalent finite element method allows a decomposition of the error into multiple components, each describing the effect of a different portion of the method on the total error in a quantity-of-interest.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L70 Error bounds for numerical methods for ordinary differential equations
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