CONTROL OF ACCURACY OF TAYLOR-COLLOCATION METHOD TO SOLVE THE WEAKLY REGULAR VOLTERRA INTEGRAL EQUATIONS OF THE FIRST KIND BY USING THE CESTAC METHOD

摘要

Finding the optimal parameters and functions of iterative methods are among the main problems of the Numerical Analysis. For this aim, a technique of the stochastic arithmetic (SA) is used to control of accuracy of Taylor-collocation method for solving first kind weakly regular integral equations (IEs). Thus, the CESTAC (Controle et Estimation Stochastique des Arrondis de Calculs) method and the CADNA (Control of Accuracy and Debugging for Numerical Applications) library are applied. By using this method the optimal iteration of Taylor-collocation method, the optimal error and the optimal approximation to solve the weakly regular IEs of the first kind can be obtained. They are the main differences of the SA in comparison with other methods based on the floating point arithmetic (FPA). Some examples are solved by using the Taylor-collocation method based on the CESTAC method and the numerical results are demonstrated in several tables.