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Some numerical efficiency estimates for the transformation of the Cauchy problem for differential equations to the best argument. (English. Russian original) Zbl 0977.34004
Comput. Math. Math. Phys. 39, No. 7, 1092-1099 (1999); translation from Zh. Vychisl. Mat. Mat. Fiz. 39, No. 7, 1134-1141 (1999).
Summary: An analytic transformation [E. B. Kuznetsov and V. I. Shalashilin, Comput. Math. Math. Phys. 33, No. 12, 1569-1579 (1993); translation from Zh. Vychisl. Mat. Mat. Fiz. 33, No. 12, 1792-1805 (1993; Zbl 0818.65062)] suggested previously for problems that can be reduced to the construction of a continuous one-parametric set of solutions is applied to the Cauchy problem for ordinary differential equations. Numerical estimates for the influence of the transformation on the local error and the stability of numerical integration methods are obtained. The influence exerted by the transformation on the efficiency of the methods is analyzed using particular examples.
MSC:
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
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