Abstract. In this paper, we propose a numerical solver for initial value problems of ordinary differential equations using the IMT-DE type numerical indefinite integration formula. In the presented method, we consider the Picard iterative solutions for an integral equation equivalent to the initial value problem and obtain a numerical solution approximating the integral operator appearing in the iterative solutions by the IMT-DE formula. In addition, the iteration is accelerated by the update used in the Gauss-Seidel method for linear systems. A theoretical error analysis and numerical examples show the effectiveness of the presented method.

Abstract. The movement to turf school grounds is gaining momentum, although cost is a major issue. Low-cost turf planting can be realized by devising the planting methods. In this study, we describe the growth process of turfgrass as mathematical models and show the usefulness of the planting through the numerical simulations. When the parameters based on practice are determined for the Lotka-Volterra equation with time-dependent growth coefficients, numerical results explaining the lower cost were obtained. Therefore the validity of the planting practice based on this study was confirmed.