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Explicit Runge-Kutta methods have been studied for over a century and have applications in the sciences as well as mathematical software such as Matlab’s ode45 solver. We have taken a new look at fourthand fifth-order Runge-Kutta methods by utilizing techniques based on Gröbner bases to design explicit fourth-order Runge-Kutta formulas with step doubling(More)
Lumbago is one of the most prevalent symptoms in patients with osteoporotic vertebral fracture. Roland-Morris Disability Questionnaire (RDQ) is a quality of life (QOL) questionnaire targeted for evaluating lumbago. Although total score is the usual way of analysis, we have tried to make more use of it by subscale analysis. Forty-four osteoporotic patients(More)
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