Search Results - "Verner, J. H."

Nullspaces yield new explicit Runge–Kutta pairs by Verner, J. H.

“…Sixty years ago, Butcher (Butcher Math. Soc. 3, 185–201 1963) characterized a natural tabulation of the order conditions for Runge–Kutta methods of order p as…”
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Numerically optimal Runge–Kutta pairs with interpolants by Verner, J. H.

“…Explicit Runge–Kutta pairs are known to provide efficient solutions to initial value differential equations with inexpensive derivative evaluations. Two…”
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Explicit Runge–Kutta pairs with lower stage-order by Verner, J. H.

“…Explicit Runge–Kutta pairs of methods of successive orders of accuracy provide effective algorithms for approximating solutions to nonstiff initial value…”
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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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Derivation and implementation of Two-Step Runge-Kutta pairs by Jackiewicz, Z., Verner, J. H.

“…Explicit Runge-Kutta pairs are known to provide efficient solutions to initial value differential equations with inexpensive derivative evaluations. Two-step…”
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Subquadrature expansions for TSRK methods by Kværnø, Anne, Verner, J. H.

“…The representation of order conditions for general linear methods formulated using an algebraic theory by Butcher, and the alternative using B-series by Hairer…”
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Differentiable Interpolants for High-Order Runge-Kutta Methods by Verner, J. H.

“…For a particular family of pairs of explicit Runge-Kutta methods of orders p - 1 and p, sets of efficient, continuously differentiable interpolants of several…”
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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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Some Runge-Kutta Formula Pairs by Verner, J. H.

“…In ["The Numerical Analysis of Ordinary Differential Equations," John Wiley, New York, 1987, pp. 298-303], Butcher derives a family of nine-stage formula pairs…”
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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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Explicit Runge-Kutta Methods with Estimates of the Local Truncation Error by Verner, J. H.

“…Efficient algorithms for the approximate solution of ordinary differential equations rely on controlling estimates of the error through adjustment of stepsize…”
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A Contrast of Some Runge-Kutta Formula Pairs by Verner, J. H.

“…Fehlberg [Computing, 4 (1969), pp. 93-106] developed a family of eight-stage pairs of Runge-Kutta methods of orders 5 and 6. Subsequently, improved versions…”
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Completely Imbedded Runge-Kutta Pairs by Sharp, P. W., Verner, J. H.

“…Recently, pairs of explicit Runge-Kutta methods of orders 5 and 6 based on a new design have been derived independently by several authors. These pairs may be…”
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Families of Imbedded Runge-Kutta Methods by Verner, J. H.

“…Using the s stages of an explicit Runge-Kutta method of order p, approximations of various lower orders may be obtained. A linear system of equations…”
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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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Continuous Explicit Runge-Kutta Methods of Order 5 by Verner, J. H., Zennaro, M.

“…A continuous explicit Runge-Kutta (CERK) method provides a continuous approximation to an initial value problem. Such a method may be obtained by appending…”
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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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Quadratures for Implicit Differential Equations by Verner, J. H.

“…Quadrature methods are used to obtain numerical solutions of certain systems of implicit differential equations. Development of the methods leads to an…”
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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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