A spectral Rayleigh–Ritz scheme for nonlinear partial differential systems of first order
Hussien, H. (2016). A spectral Rayleigh–Ritz scheme for nonlinear partial differential systems of first order. EKB Journal Management System, 24(3), 373-380. doi: 10.1016/j.joems.2015.11.001
Hussien S. Hussien. "A spectral Rayleigh–Ritz scheme for nonlinear partial differential systems of first order". EKB Journal Management System, 24, 3, 2016, 373-380. doi: 10.1016/j.joems.2015.11.001
Hussien, H. (2016). 'A spectral Rayleigh–Ritz scheme for nonlinear partial differential systems of first order', EKB Journal Management System, 24(3), pp. 373-380. doi: 10.1016/j.joems.2015.11.001
Hussien, H. A spectral Rayleigh–Ritz scheme for nonlinear partial differential systems of first order. EKB Journal Management System, 2016; 24(3): 373-380. doi: 10.1016/j.joems.2015.11.001

A spectral Rayleigh–Ritz scheme for nonlinear partial differential systems of first order

Journal of the Egyptian Mathematical Society
Volume 24, Issue 3, 2016, Pages 373-380    PDF (1.19 M)
DOI: 10.1016/j.joems.2015.11.001
Author
Hussien S. Hussien
Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, Egypt
Abstract
Nonlinear systems of partial differential problems of first order with Dirichlet boundary
conditions is considered. ultraspherical integral zero- boundary (UIZB) method is combined with
Rayleigh–Ritz method to approximate the unknowns. The approach converts the problem to be a
multi-objective constrained optimization problem which is easier to solve. Accurate results can be
obtained by selecting a limited number of collocation points. Numerical examples are included to
demonstrate the accuracy and efficiency of the propped method.
Keywords
Ultraspherical integral ze- ros method; Rayleigh–Ritz method; Boundary value problems; Nonlinear first-order par- tial differential systems; Multi-objective constrained optimization
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