caa a22 4500 605497001 CHVBK 20210128100539.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10543-015-0544-2 doi (NATIONALLICENCE)springer-10.1007/s10543-015-0544-2 Behroozifar Mahmoud Faculty of Basic Sciences, Babol University of Technology, 47148-71167, Babol, Mazandaran, Iran aut Spectral method for solving high order nonlinear boundary value problems via operational matrices [Elektronische Daten] [Mahmoud Behroozifar] A spectral method based on operational matrices of Bernstein polynomials using collocation method is elaborated and employed for solving nonlinear ordinary and partial differential equations with multi-point boundary conditions. First, properties of Bernstein polynomial, operational matrices of integration, differentiation and product are introduced and then utilized to reduce the given differential equation to the solution of a system of algebraic equations. This new approach provides a significant computational advantage by converting the given original problem to an equivalent integro-differential equation which implies all boundary condition. Approximate solution is achieved by expanding the desired function in terms of a Bernstein basis and employing operational matrices. Unknown coefficients are determined by collocation. The method is compared with modified Adomian decomposition method, Birkhoff-type interpolation method, reproducing kernel Hilbert space method, fixed point method, finite-difference Keller-box method, multilevel augmentation method and shooting method. Illustrative examples are included to demonstrate the high precision, validity and good performance of the new scheme even for solving nonlinear singular differential equations. Springer Science+Business Media Dordrecht, 2015 Nonlinear differential equations nationallicence Multi-point boundary value problem nationallicence Bernstein basis nationallicence Operational matrix nationallicence Collocation spectral method nationallicence BIT Numerical Mathematics Springer Netherlands 55/4(2015-12-01), 901-925 0006-3835 55:4<901 2015 55 10543 https://doi.org/10.1007/s10543-015-0544-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10543-015-0544-2 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Behroozifar Mahmoud Faculty of Basic Sciences, Babol University of Technology, 47148-71167, Babol, Mazandaran, Iran aut NATIONALLICENCE 773 0- BIT Numerical Mathematics Springer Netherlands 55/4(2015-12-01), 901-925 0006-3835 55:4<901 2015 55 10543