Choice of Collocation Points for Axisymmetric Nonlinear Two-Point Boundary Value Problems In Statics Of Shallow Spherical Shells - Nath, Y.; Dumir, P.C.; Gandhi, M.L. (Engineering Transactions, 1983)
The present work investigates the optimum choice of collocation points which gives for а given accuracy the minimum number of collocation points. А convergence study has been conducted for the axisymmetric nonlinear analysis of а shallow spherical shell under а uniformly distributed Joad with four different choices of collocation points, viz. equidistant collocation points; collocation at maxima of а Chebysbev polynomial; collocation at zeros of а Chebyshev polynomial and zeros of а Legendre polynomial (Gaussian points) as collocation points. It has been found that the Gaussian collocation method has the fastest rate of convergence and it yields accurate results even with small numbеr of collocation points. Тhе results for the nonlinear static analysis of elastic circular plates апd shallow spherical shells obtained bу the Gaussiau collocation method hаvе been presented and аre found to be in good agreement with the гesults available.