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.
Hussien, H. (2016). A spectral Rayleigh–Ritz scheme for nonlinear partial differential systems of first order. Journal of the Egyptian Mathematical Society, 24(3), 373-380. doi: 10.1016/j.joems.2015.11.001
MLA
Hussien S. Hussien. "A spectral Rayleigh–Ritz scheme for nonlinear partial differential systems of first order", Journal of the Egyptian Mathematical Society, 24, 3, 2016, 373-380. doi: 10.1016/j.joems.2015.11.001
HARVARD
Hussien, H. (2016). 'A spectral Rayleigh–Ritz scheme for nonlinear partial differential systems of first order', Journal of the Egyptian Mathematical Society, 24(3), pp. 373-380. doi: 10.1016/j.joems.2015.11.001
VANCOUVER
Hussien, H. A spectral Rayleigh–Ritz scheme for nonlinear partial differential systems of first order. Journal of the Egyptian Mathematical Society, 2016; 24(3): 373-380. doi: 10.1016/j.joems.2015.11.001
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