A family of multivalue collocation methods for the numerical solution of differential problems is proposed. These methods are developed in order to be suitable for the solution of stiff problems, since they are highly stable and do not suffer from order reduction, as they have uniform order of convergence in the whole integration interval. In addition, they permits to have an efficient implementation, due to the fact that the coefficient matrix of the nonlinear system for the computation of the internal stages has a lower triangular structure with one-point spectrum. The uniform order of convergence is numerically computed in order to experimentally verify theoretical results.
One-point spectrum Nordsieck almost collocation methods
Conte Dajana;D'arienzo Maria Pia;Paternoster Beatrice
2020-01-01
Abstract
A family of multivalue collocation methods for the numerical solution of differential problems is proposed. These methods are developed in order to be suitable for the solution of stiff problems, since they are highly stable and do not suffer from order reduction, as they have uniform order of convergence in the whole integration interval. In addition, they permits to have an efficient implementation, due to the fact that the coefficient matrix of the nonlinear system for the computation of the internal stages has a lower triangular structure with one-point spectrum. The uniform order of convergence is numerically computed in order to experimentally verify theoretical results.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
