In this paper, we study an efficient asymptotically correction of a-posteriori er- ror estimator for the numerical approximation of Volterra integro-differential equations by piecewise polynomial collocation method. T...In this paper, we study an efficient asymptotically correction of a-posteriori er- ror estimator for the numerical approximation of Volterra integro-differential equations by piecewise polynomial collocation method. The deviation of the error for Volterra integro- differential equations by using the defect correction principle is defined. Also, it is shown that for m degree piecewise polynomial collocation method, our method provides O（hm＋l） as the order of the deviation of the error. The theoretical behavior is tested on examples and it is shown that the numerical results confirm the theoretical part.展开更多
文摘In this paper, we study an efficient asymptotically correction of a-posteriori er- ror estimator for the numerical approximation of Volterra integro-differential equations by piecewise polynomial collocation method. The deviation of the error for Volterra integro- differential equations by using the defect correction principle is defined. Also, it is shown that for m degree piecewise polynomial collocation method, our method provides O（hm＋l） as the order of the deviation of the error. The theoretical behavior is tested on examples and it is shown that the numerical results confirm the theoretical part.
