Abstract
A class of methods for solving the initial value problem for ordinary differential equations is studied. We developr-block implicit one-step methods which compute a block ofr new values simultaneously with each step of application. These methods are examined for the property ofA-stability. A sub-class of formulas is derived which is related to Newton-Cotes quadrature and it is shown that for block sizesr=1,2,..., 8 these methods areA-stable while those forr=9,10 are not. We constructA-stable formulas having arbitrarily high orders of accuracy, even stiffly (strongly)A-stable formulas.
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Watts, H.A., Shampine, L.F. A-stable block implicit one-step methods. BIT 12, 252–266 (1972). https://doi.org/10.1007/BF01932819
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DOI: https://doi.org/10.1007/BF01932819