Efficient implementation of Radau collocation methods

Parallel Implementation of Collocation Methods

Collocation methods: More efficient procedures for applying collocation

In recent years, new and more effective procedures for applying collocation have been published. This article is devoted to present a revision of this subject and complement its developments. From the general theory two broad approaches are derived, which yield the direct and the indirect TH-collocation methods. The former approach had not been published before, and it is a dual of the indirect...

Efficient Embedded Formula for Chebyshev Collocation Methods

In this talk, we are concerned with embedded formulae of the Chebyshev collocation methods [1] developed recently. We introduce two Chebyshev collocation methods based on generalized Chebyshev interpolation polynomials [2], which are used to make an automatic integration method. We apply an elegant algorithm of generalized Chebyshev interpolation increasing the node points to make an error esti...

Aggregation methods for efficient collocation detection

In this article we propose a rank aggregation method for the task of collocations detection. It consists of applying some well-known methods (e.g. Dice method, chi-square test, z-test and likelihood ratio) and then aggregating the resulting collocations rankings by rank distance and Borda score. These two aggregation methods are especially well suited for the task, since the results of each ind...

THE COMPARISON OF EFFICIENT RADIAL BASIS FUNCTIONS COLLOCATION METHODS FOR NUMERICAL SOLUTION OF THE PARABOLIC PDE’S

In this paper, we apply the compare the collocation methods of meshfree RBF over differential equation containing partial derivation of one dimension time dependent with a compound boundary nonlocal condition.