Volume 11, Issue 4 (2000), pp. 371–380
The accuracy of adaptive integration algorithms for solving stiff ODE is investigated. The analysis is done by comparing the discrete and exact amplification factors of the equations. It is proved that the usage of stiffness number of the Jacobian matrix is sufficient in order to estimate the complexity of solving ODE problems by explicit integration algorithms. The complexity of implicit integration algorithms depends on the distribution of eigenvalues of the Jacobian. Results of numerical experiments are presented.
Volume 8, Issue 2 (1997), pp. 273–288
In this paper, the following questions for computing coefficients of Fourier series are discussed: n-order Filon quadrature formula and its partial cases, some features of applying the Filon method in computing coefficients when the adaptive integration strategy is employed, the program implementation of 3-order and 5-order Filon quadrature formulas, using the adaptive integration strategy, and the experimental results of applying them in computing coefficients of Fourier series.