Efficient Estimation of Lucas Polynomial Derivatives through Combined BVP and IVP

Document Type : Original Article

Authors

1 Mathematics department, Faculty of Science, Zagazig university, Zagazig, Egypt.

2 Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt

3 Mathematics Department, High Institute of Information and Technology, October, Cairo, Egypt.

4 Mathematics department , faculty of science , Zagazig university, Zagazig, Egypt.

Abstract

This paper delves into the study of Lucas polynomials (LP) through the significant tau method for constructing an approximate semi-analytic technique for linear and non-linear ordinary differential equations (ODEs). Two proposed schemes are generated by the operational matrices of derivatives of LP to convert the proposed equations to matrix-equations. The Lane-Emden equations are mainly application in this study. The Lane-Emden equation is a mathematical model of ODEs used in astrophysics to describe the structure of stars and other spherically symmetric objects. Its journey has been fascinating and intertwined with the development of our understanding of stellar evolution. The extracted results, presented with both numerical and graphical representations, provide evidence for the accuracy and solution efficiency of the proposed schemes. These results illustrate the accuracy and efficiency of the new methods in comparison with existing techniques, highlighting their potential for advancing both theoretical and practical applications in differential equations and astrophysical modeling.

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