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Creators/Authors contains: "Seibold, Benjamin"

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  1. ; ; ; ; (, SIAM Journal on Numerical Analysis)
    Explicit Runge--Kutta (RK) methods are susceptible to a reduction in the observed order of convergence when applied to an initial boundary value problem with time-dependent boundary conditions. We study conditions on explicit RK methods that guarantee high order convergence for linear problems; we refer to these conditions as weak stage order conditions. We prove a general relationship between the method's order, weak stage order, and number of stages. We derive explicit RK methods with high weak stage order and demonstrate, through numerical tests, that they avoid the order reduction phenomenon up to any order for linear problems and up to order three for nonlinear problems. 
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    Free, publicly-accessible full text available August 31, 2026
  2. ; ; ; (, SIAM Journal on Numerical Analysis)
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  3. ; ; ; (, Communications in Mathematical Sciences)
    This paper studies the spatial manifestations of order reduction that occur when timestepping initial-boundary-value problems (IBVPs) with high-order Runge–Kutta methods. For such IBVPs, geometric structures arise that do not have an analog in ODE IVPs: boundary layers appear, induced by a mismatch between the approximation error in the interior and at the boundaries. To understand those boundary layers, an analysis of the modes of the numerical scheme is conducted, which explains under which circumstances boundary layers persist over many time steps. Based on this, two remedies to order reduction are studied: first, a new condition on the Butcher tableau, called weak stage order, that is compatible with diagonally implicit Runge–Kutta schemes; and second, the impact of modified boundary conditions on the boundary layer theory is analyzed. 
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  4. ; ; ; ; ; ; ; ; ; ; et al (, IEEE)
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  5. ; ; ; (, Communications in Applied Mathematics and Computational Science)
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  6. ; ; ; ; ; (, 2022 International Conference on Robotics and Automation (ICRA))
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  7. ; ; ; (, Computer Methods in Applied Mechanics and Engineering)
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  8. ; ; ; ; ; ; ; ; ; (, IFAC-PapersOnLine)
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  9. ; ; (, Journal of Computational Physics)
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  10. ; ; ; (, Journal of Computational and Applied Mathematics)
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