New fifth-order Runge-Kutta formulas of classical type are exhibited. Some are special cases of the family due to Kutta, but require fewer multiplications and lead to less error than those commonly used. In addition, two new families of solutions are presented, some of whose members have similar properties. Included are extensions of Radau, Lobatto, Newton-Cotes and Legendre-Gauss quadratures.
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Luther et al. (1965) studied this question.
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