Toshio Fukushima

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K e y w o r d s O b r e c h k o f f methods, Super-implicit method, Initial value problems. 1: I N T R O D U C T I O N In th is paper , we discuss t h e numer ica l so lu t ion of f i rs t -order ini t ia l va lue p rob l ems ( IVPs) y'(x) = f ( x , y(~)) , y(0) = y0, (1) and a specia l class (for which yl is miss ing) of second-order I V P s y ' ( x ) = f(More)
We present a numerical method to invert a general incomplete elliptic integral with respect to its argument and/or amplitude. The method obtains a solution by bisection accelerated by the half argument formulas and the addition theorems to evaluate the incomplete elliptic integrals and Jacobian elliptic functions required in the course. If a faster(More)
We developed a new method to compute the cosine amplitude function, c ≡ cn(u|m), by using its double argument formula. The accumulation of roundoff errors is effectively suppressed by the introduction of a complementary variable, b ≡ 1− c, and a conditional switch between the duplication of b and c. The sine and delta amplitude functions, s ≡ sn(u|m) and d(More)
We developed a novel method to calculate an associate complete elliptic integral of the third kind, J(n|m) ≡ [Π (n|m) − K(m)]/n. The key idea is the double argument formula of J(n|m) with respect to n. We derived it from the not-so-popular addition theorem of Jacobi’s complete elliptic integral of the third kind, Π1(a|m), with respect to a, which is a real(More)