A Method for the Numerical Integration of Ordinary Differential Equations
نویسنده
چکیده
where y(x) denotes the solution of the differential equation. The idea is to use a quadrature formula to estimate the integral of (1). This requires knowledge of the integrand at specified arguments x¿ in (xo, -To + h)—hence we require the values of y(x) at these arguments. A numerical integration method may be used to estimate y(x) for the required arguments. In this way a numerical integration method is combined with a quadrature formula to obtain another numerical integration method. A large number of methods may be devised, depending on which combination of quadrature formula and integration method is used. In particular, the Gauss two-point quadrature formula combined with the Runge-Kutta fourth order method appears to give excellent results [1]. We propose here the combination of the Radau three-point quadrature formula with the Runge-Kutta fourth order method. The resulting method seems to give greater accuracy with the same amount of work. 2. The Method. The Radau quadrature formula [2] gives
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