New ultraspherical wavelets collocation method for solving 2nth-order initial and boundary value problems | ||
| Journal of the Egyptian Mathematical Society | ||
| Volume 24, Issue 2, 2016, Pages 319-327 PDF (593.39 K) | ||
| DOI: 10.1016/j.joems.2015.05.002 | ||
| Authors | ||
| E. H. Doha1; W. M. Abd-Elhameed1, 2; Y. H. Youssri1 | ||
| 1Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt | ||
| 2Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah, Saudi Arabia | ||
| Abstract | ||
| In this paper, a new spectral algorithm based on employing ultraspherical wavelets along with the spectral collocation method is developed. The proposed algorithm is utilized to solve linear and nonlinear even-order initial and boundary value problems. This algorithm is supported by study- ing the convergence analysis of the used ultraspherical wavelets expansion. The principle idea for obtaining the proposed spectral numerical solutions for the above-mentioned problems is actually based on using wavelets collocation method to reduce the linear or nonlinear differential equations with their initial or boundary conditions into systems of linear or nonlinear algebraic equations in the unknown expansion coefficients. Some specific important problems such as Lane–Emden and Burger’s type equations can be solved efficiently with the suggested algorithm. Some numerical ex- amples are given for the sake of testing the efficiency and the applicability of the proposed algorithm | ||
| Keywords | ||
| Ultraspherical polynomials; Wavelets; Bernstein-type inequality; Collocation method; Even-order differential equations; Burger’s equation | ||
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