  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
