Search Results - "Verner, J.H."

Improved starting methods for two-step Runge–Kutta methods of stage-order by Verner, J.H.

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Starting methods for two-step Runge–Kutta methods of stage-order 3 and order 6 by Verner, J.H.

“…Jackiewicz and Tracogna [SIAM J. Numer. Anal. 32 (1995) 1390–1427] proposed a general formulation of two step Runge–Kutta (TSRK) methods. Using formulas for…”
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Improved starting methods for two-step Runge–Kutta methods of stage-order p − 3 by Verner, J.H.

“…In [Japan JIAM 19 (2002) 227], Jackiewicz and Verner derived formulas for, and tested the implementation of two-step Runge–Kutta (TSRK) pairs. For pairs of…”
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Global Error Estimators for Order 7, 8 Runge–Kutta Pairs by Macdougall, T, Verner, J.H

“…Dormand, Prince and their colleagues [3–5] showed in a sequence of papers that the approximation of an initial value differential system propagated by a…”
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High-order explicit Runge-Kutta pairs with low stage order by Verner, J.H.

“…To illustrate his idea for propagating an approximate solution of an initial value problem, Runge (1895) included a pair of formulas or orders 1 and 2 (a 1,2…”
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Some Extended Explicit Bel'Tyukov Pairs for Volterra Integral Equations of the Second Kind by Sharp, P.W., Verner, J.H.

“…We derive and investigate a family of pairs of extended explicit Bel'tyukov Runge-Kutta (EBVRK) formulas to treat Volterra integral equations of the second…”
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Graphs with the same determinant as a complete graph by Olesky, D.D., van den Driessche, P., Verner, J.H.

“…A family of n×n symmetric circulant (0, 1) matrices is studied. It is shown that the determinant of each matrix is (−1) n−1(n−1) , a property shared with the…”
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Extended explicit Bel'tyukov pairs of orders 4 and 5 for Volterra integral equations of the second kind by Sharp, P.W., Verner, J.H.

“…The derivation of extended explicit Bel'tyukov pairs of methods for Volterra integral equations of the second kind is related to that of explicit Runge–Kutta…”
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