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- W1978260458 abstract "We apply Runge–Kutta methods to linear partial differential-algebraic equations of the form Aut(t,x)+B(uxx(t,x)+rux(t,x))+Cu(t,x)=f(t,x), where A,B,C∈Rn,n and the matrix A is singular. We prove that under certain conditions the temporal convergence order of the fully discrete scheme depends on the time index of the partial differential-algebraic equation. In particular, fractional orders of convergence in time are encountered. Furthermore we show that the fully discrete scheme suffers an order reduction caused by the boundary conditions. Numerical examples confirm the theoretical results." @default.
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- W1978260458 date "2005-05-01" @default.
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- W1978260458 title "Convergence of Runge–Kutta methods applied to linear partial differential-algebraic equations" @default.
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- W1978260458 doi "https://doi.org/10.1016/j.apnum.2004.08.023" @default.
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