New wavelet method based on Shifted Lucas polynomials: A tau approach

Abstract: In current work, non-familiar shifted Lucas polynomials are introduced. We have constructed a computational wavelet technique for solution of initial/boundary value second order differential equations. For this numerical scheme, we have developed weight function and Rodrigues' formula for Lucas polynomials. Further, Lucas polynomials and their properties are used to propose shifted Lucas polynomials and then utilization of shifted Lucas polynomials provides us shifted Lucas wavelet. We furnished the operational matrix of differentiation and the product operational matrix of the shifted Lucas wavelets. Moreover, convergence and error analysis ensure accuracy of the proposed method. Illustrative examples show that the present method is numerically fruitful, effective and convenient for solving differential equations