# A Stiff MOL Boundary Control Problem for the 1D Heat Equation with Exact Discrete Solution

@article{Lang2022ASM, title={A Stiff MOL Boundary Control Problem for the 1D Heat Equation with Exact Discrete Solution}, author={Jens Lang and Bernhard A. Schmitt}, journal={ArXiv}, year={2022}, volume={abs/2209.14051} }

Method-of-lines discretizations are demanding test problems for stiﬀ integration methods. However, for PDE problems with known analytic solution the presence of space discretization errors or the need to use codes to compute reference solutions may limit the validity of numerical test results. To over-come these drawbacks we present in this short note a simple test problem with boundary control, a situation where one-step methods may suﬀer from order reduction. We derive exact formulas for the…

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