Abstract
AbstractNew high‐order Runge‐Kutta formulas for systems of first‐ and second‐order differential equations are derived. These new formulas, although similar to earlier formulas of the author, offer the advantage of a greatly reduced truncation error. By the proper choice of a parameter the leading term of the truncation error can be made arbitrarily small (but not zero) without increase of the overall computational expense per step, as compared with the earlier formulas. 24‐digit tables for the new Runge‐Kutta coefficients are presented for 8‐th through 12‐th order formulas. Two examples demonstrate the advantage of the new formulas as expressed in a substantial reduction of the number of required integration steps and, therefore, of the total computer running time as well.
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Schedule a callMore From: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
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