Rational Runge-Kutta methods for solving systems of ordinary differential equations

Computing - Tập 20 - Trang 333-342 - 1978
A. Wambecq1
1Applied Mathematics and Programming Division, K. U. Leuven, Heverlee, Gelgium

Tóm tắt

Some nonlinear methods for solving single ordinary differiential equations are generalized to solve systems of equations. To perform this, a new vector product, compatible with the Samelson inverse of a vector, is defined. Conditions for a given order are derived.

Tài liệu tham khảo

Padé, H.: Sur la représentation approchée d'une fonction par des fractions rationelles. Am. Sci. Ecole Normale Supér.9, 1–92 (1892). Merson, R. H.: An operational method for the study of investigration processes, Proceedings of a symposiusm on data processing and Automatic Computing Machines at Weapons Research Establishment (1957), Salisbury, Australia. Paper No. 110. Wynn, P.: Acceleration Techniques for Iterated vector and Matrix Problems. Math. Comp.16, 322 (1962). Butcher, J. C.: Coefficients for the study of Runge-Kutta integration processes. J. Aust. Math. Soc.3, 185–201 (1963). Butcher, J. C.: Implicit Runge-Kutta processes. Math. Comp.18, 50–64 (1964). Scraton, R. E.: Estimation of the truncation error in Runge-Kuta and allied processes. The Computer Journal7, 245–248 (1964). Butcher, J. C.: On the attainable order of Runge-Kutta methods. Math. Comp.19 408–417 (1965). Lambert, J. D., Shaw, B.: On the numerical solution ofy′=f(x, y) by a class of formulae based on rational approximation. Math. Comp.19, 456–462 (1965). Curtis, A. R.: Letter to the Editor. The Computer Journal8, 52 (1965). Gragg, W. B.: The Padé table and its relation to certain algorithms of numerical analysis. SIAM Review14, 1–62 (1972). Lambert, J. D.: The unconvential classes of methods for stiff systems, in: Stiff Differential Equations (Willoughby, R., ed.), pp. 171–186. 1974. Lambert, J. D.: Computational methods in ordinary differential equations. London: J. Wiley 1974. Wambecq, A.: Nonlinear methods in solving ordinary differential equations. J. Comp. Appl. Math.2, 27–33 (1976). Gear, G. W.: Numerical initial valu9e problems in ordinary differential equations, pp. 218–219. Englewood Cliffs, N. J.: Prentice-Hall 1971.