Indirect methods of collocation: Trefftz-Herrera collocation

✍ Scribed by Ismael Herrera; Martín Díaz

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 280 KB
• Volume: 15
• Category: Article
• ISSN: 0749-159X
• DOI: 10.1002/(sici)1098-2426(199911)15:6<709::aid-num7>3.0.co;2-x

✦ Synopsis

A nonstandard collocation method (TH-collocation) is presented, where collocation is used to construct specialized weighting functions instead of the solution itself, as it is usual, so that in this sense it is an indirect method. TH-collocation is shown to be as accurate as standard collocation, but computationally far more efficient. The present article is the first of a series devoted to explore thoroughly collocation methods. The following classification of collocation methods is introduced: direct-nonoverlapping; indirectnonoverlapping; direct-overlapping; and indirect-overlapping. Most of the effort reported in the literature has gone to direct-nonoverlapping methods. The procedure presented in this article falls into the indirectnonoverlapping category and it is based on Trefftz-Herrera formulation.