Block-pentadiagonal system

An obvious extension of the above method to higher order formulas is to use more points in the approximation of the spatial derivatives. These ideas lead to the well-known five-point discretization of fourth order. Unfortunately, for implicit integration a block-pentadiagonal system has to be solved now. In addition, the boundaries need a special treatment that leads to an even larger bandwidth of the matrices or to a decrease of the approximation order at the boundaries. 

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