Problems of convergence of the direct methods of numerical solution of singular integral equations with Cauchy-type kernels
Problems of convergence of the direct methods of numerical solution of singular integral equations with Cauchy-type kernels
In this technical report, general directions are given for the proof of the convergence of four direct methods of numerical solution of real Cauchy-type singular integral equations on a finite open interval. The methods under consideration are (i) the Galerkin method, (ii) the collocation method, (iii) the quadrature–collocation method and (iv) the quadrature method. It is believed that the given directions can really be applied to the detailed and rigorous proof of the convergence of the aforementioned methods as well as of additional related or even more general methods.
- University of Patras Greece
Σύγκλιση, Numerical solution, Cauchy-type singular integral equations, Μέθοδος συντοπισμού, Μέθοδος αριθμητικής ολοκληρώσεως, Quadrature–collocation method, 510, Ιδιόμορφες ολοκληρωτικές εξισώσεις τύπου Cauchy, Μέθοδος Galerkin, Direct methods, Άμεσες μέθοδοι, Quadrature method, Μέθοδος αριθμητικής ολοκληρώσεως–συντοπισμού, Convergence, Galerkin method, Collocation method, Αριθμητική επίλυση
Σύγκλιση, Numerical solution, Cauchy-type singular integral equations, Μέθοδος συντοπισμού, Μέθοδος αριθμητικής ολοκληρώσεως, Quadrature–collocation method, 510, Ιδιόμορφες ολοκληρωτικές εξισώσεις τύπου Cauchy, Μέθοδος Galerkin, Direct methods, Άμεσες μέθοδοι, Quadrature method, Μέθοδος αριθμητικής ολοκληρώσεως–συντοπισμού, Convergence, Galerkin method, Collocation method, Αριθμητική επίλυση
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