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