Unconditionally stable higher-order accurate collocation time-step integration algorithms for first-order equations

✍ Scribed by T.C. Fung

• Book ID: 104266633
• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 136 KB
• Volume: 190
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(00)00193-6

✦ Synopsis

In this paper, unconditionally stable higher-order accurate time-step integration algorithms for linear ®rst-order dierential equations based on the collocation method are presented. The ampli®cation factor at the end of the spectrum is a controllable algorithmic parameter. The collocation parameters for unconditionally stable higher-order accurate algorithms are found to be given by the roots of a polynomial in terms of the ultimate ampli®cation factor. In general, when the numerical solution is approximated by a polynomial of degree n, this approximation is at least nth order accurate. However, by using the above collocation parameters, the order of accuracy can be improved to 2n À 1 or 2n. The approximate solutions are found to be equivalent to the generalized Pad e approximations. Furthermore, it is shown that the accuracy of the particular solution due to excitation given by the present method is compatible with the homogeneous solutions. No modi®cation of the collocation parameters is required.