The numerical solution of differential-algebraic systems using Runge Kutta methods of special type
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In this dissertation we are concerned with the solution of differential-algebraic equations using Runge Kutta methods whose coefficient matrices are singular. Not all such Runge Kutta methods are well defined when applied to differential-algebraic equations; however, Runge Kutta methods of special type are shown here to be well defined when applied to either constant coefficient or uniform index 1 differential-algebraic equations. We also derive conditions on the coefficients of such a method sufficient for any desired order.