Study of Spline Collocation Method and its Application on Engineering Problems
Date Issued
2009
Date
2009
Author(s)
Huang, Hsu-Hui
Abstract
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.
Subjects
spline collocation method (SCM)
radial spline collocation method (RSCM)
spline collocation element method (SCEM)
Type
thesis
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