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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)
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 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)