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- T. FUKUSHIMA
- 2003

This paper discusses the numerical solution of first-order initial value problems and a special class of second-order ones (those not containing first derivative). Two classes of methods are discussed, super-implicit and Obrechkoff. We will show equivalence of super-implicit and Obrechkoff schemes. The advantage of Obrechkoff methods is that they are… (More)

- Toshio Fukushima
- J. Computational Applied Mathematics
- 2011

- Toshio Fukushima
- 2012

As a preparation step to compute Jacobian elliptic functions efficiently, we created a fast method to calculate the complete elliptic integral of the first and second kinds, K(m) and E(m), for the standard domain of the elliptic parameter, 0 < m < 1. For the case 0 < m < 0.9, the method utilizes 10 pairs of approximate polynomials of the order of 9 to 19… (More)

- Toshio Fukushima
- Numerische Mathematik
- 2010

- Toshio Fukushima
- J. Computational Applied Mathematics
- 2013

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)

- Toshio Fukushima
- J. Computational Applied Mathematics
- 2012

- Toshio Fukushima
- Math. Comput.
- 2012

- Toshio Fukushima
- Numerische Mathematik
- 2013

- Toshio Fukushima
- J. Computational Applied Mathematics
- 2013

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, Π 1 (a|m), with respect to a, which is a… (More)

- Toshio Fukushima
- J. Computational Applied Mathematics
- 2013