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Two spectral Legendre's derivative algorithms for Lane-Emden, Bratu equations, and singular perturbed problems.
- Source :
-
Applied Numerical Mathematics . Nov2021, Vol. 169, p243-255. 13p. - Publication Year :
- 2021
-
Abstract
- This research aims to assemble two methodical spectral Legendre's derivative algorithms to numerically attack the Lane-Emden, Bratu's, and singularly perturbed type equations. We discretize the exact unknown solution as a truncated series of Legendre's derivative polynomials. Then, via tau and collocation methods for linear and nonlinear problems, respectively, we obtain linear/nonlinear systems of algebraic equations in the unknown expansion coefficients. Finally, with the aid of the Gaussian elimination technique in the linear case and Newton's iterative method for the non-linear case - with vanishing initial guess- we solve these systems to obtain the desired solutions. The stability and convergence analyses of the numerical schemes were studied in-depth. The schemes are convergent and accurate. Some numerical test problems are performed to verify the efficiency of the proposed algorithms. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01689274
- Volume :
- 169
- Database :
- Academic Search Index
- Journal :
- Applied Numerical Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 151718018
- Full Text :
- https://doi.org/10.1016/j.apnum.2021.07.006