In this work results are presented from the investigation of different collocation
methods applied to solve various differential equations with boundary value
problems. For nonlinear differential problems, the Newton linearisation method
is applied. B-splines functions of order 4 and 5 in combination with two different
sets of continuity conditions are used in all the numerical approximated solutions.
Application of different collocation schemes like nonorthogonal methods
(uniformly distribution, Greville abscissae, and the maximum of B-splines) and
orthogonal collocations like Gaussian points from Legendre, Lobatto and Radau
polynomials were performed. The feasibility of collocation at Gaussian points to
solve the van der Pol equation was also verified and investigated. The results in
relation to convergence, accuracy and computational effort from all the proposed
collocation methods were compared and analysed.
to be published here soon…
21 May 2019
