Runge-Kutta interpolants for high precision computations

Runge-Kutta (RK) pairs furnish approximations of the solution of an initial value problem at discrete points in the interval of integration. Many techniques for enriching these methods with continuous approximations have been proposed. Here we constuct 8−th and 9−th order interpolation methods for a recently appeared RK pair of orders 9(8). It is the first time presented in the literature such a high accuracy dense output methods for use at quadruple precision, i.e. 32 − 33 decimal digits of accuracy. Extended numerical results justify our effort. Keywords Initial Value Problem · Dence Output · Quadruple precision. Mathematics Subject Classification (2000) MSC 65L05 · 65L06

• Type: Journal
• Year: 2007
• Where: NA
• Authors: Ch. Tsitouras
• Keywords: Furnish Approximations, Initial Value Problem, NA 2007, Quadruple Precision