Spatial Manifestations of Order Reduction in Runge-Kutta Methods for Initial Boundary Value Problems

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Rosales, Rodolfo Ruben; Seibold, Benjamin; Shirokoff, David; Zhou, Dong;
  • Subject: 65L20, 65M15, 34E05 | Mathematics - Numerical Analysis
    arxiv: Mathematics::Numerical Analysis

This paper studies the spatial manifestations of order reduction that occur when time-stepping 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... View more
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