A novel operational matrix method based on shifted Legendre polynomials for solving second-order boundary value problems involving singular, singularly perturbed and Bratu-type equations

DOI10.1007/s40096-015-0155-8zbMath1407.65080OpenAlexW1909857561WikidataQ59431518 ScholiaQ59431518MaRDI QIDQ1992168

Youssri H. Youssri, Waleed M. Abd-Elhameed, Eid H. Doha

Publication date: 2 November 2018

Published in: Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40096-015-0155-8

zbMATH Keywords

collocation methodPetrov-Galerkin methodsecond-order equationsshifted Legendre polynomialsBratu equationsingular and singularly perturbed

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Singular nonlinear boundary value problems for ordinary differential equations (34B16) Singular perturbations for ordinary differential equations (34E15)

Related Items (9)

On an operational matrix method based on generalized Bernoulli polynomials of level \(m\) ⋮ An exponential Chebyshev second kind approximation for solving high-order ordinary differential equations in unbounded domains, with application to Dawson's integral ⋮ Unnamed Item ⋮ A numerical approach for a nonhomogeneous differential equation with variable delays ⋮ Laguerre approach for solving system of linear Fredholm integro-differential equations ⋮ High-order Gegenbauer integral spectral element method integrated with an adaptive Chebyshev optimization strategy for solving linear singularly perturbed differential equations ⋮ Two spectral Legendre's derivative algorithms for Lane-Emden, Bratu equations, and singular perturbed problems ⋮ Bernstein and Gegenbauer-wavelet collocation methods for Bratu-like equations arising in electrospinning process ⋮ Spectral treatment of one and two dimensional second-order BVPs via certain modified shifted Chebyshev polynomials

Uses Software

• Matlab

Cites Work

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