Study of Spline Collocation Method and its Application on Engineering Problems

• Main Authors: Hsu-Hui Huang, 黃旭輝
• Other Authors: Lai-Yun Wu
• Format: Others
• Language: en_US
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/15672539424780408945

博士 === 國立臺灣大學 === 土木工程學研究所 === 97 === In this thesis, we study the spline collocation method (SCM), radial spline collocation method (RSCM) and spline collocation element method (SCEM) for solving engineering problems: beam, beam-column, frame, and plate problem. The popularity of the collocation method is in part due to their conceptual simplicity, wide applicability, and ease of implementation. In comparison to finite element difference methods, the CM provides approximations to the solution and its spatial derivatives at mesh point of the domain of problems. The obvious advantage of collocation method over Galerkin methods is that the calculation of the coefficients in the system of algebraic equations determining the approximate solution is very fast since no integrals need to be evaluated or approximated. Moreover, numerical experiments illustrate that the collocation method provide high order accuracy and super-convergence feature for a wide range of physical and engineering problems.