https://doi.org/10.1140/epjp/s13360-020-00865-z
Regular Article
Normalized Lucas wavelets: an application to Lane–Emden and pantograph differential equations
1
School of Mathematics, Computer and Information Sciences, Central University of Himachal Pradesh, Dharamshala, India
2
Department of Mathematics, Cankaya University, Eskisehir Yolu29.km, 06810, Ankara, Turkey
3
Institute of Space Sciences, Magurele-Bucharest, Romania
* e-mail: rakesh@cuhimachal.ac.in
Received:
8
June
2020
Accepted:
16
October
2020
Published online:
3
November
2020
In this paper, a novel normalized Lucas wavelet scheme based on tau approach is proposed for the two classes of second-order differential equations, namely Lane–Emden and pantograph equations. The introduced scheme depends on shifted Lucas polynomials (SLPs) and their operational matrix of derivative (which are developed here). The weight function for the orthogonality of Lucas polynomials, and Rodrigues formula are proposed for the first time, which form the basis for the construction of SLPs. Normalized Lucas wavelets are constructed by utilizing SLPs and their novel properties. Literally, the present scheme transforms the given method to a set of nonlinear algebraic equations with undetermined coefficients which are here tackled by tau method. Meanwhile, new treatment of convergence and error analysis is provided for the established approach. Finally, the accuracy and applicability of present scheme is ensured by considering several examples.
Key words: Rodrigues formula / Weight function / Shifted Lucas Polynomial / Wavelet / Operational matrix / Tau method
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2020