Approximation of functions with bounded derivative and solution of Riccati differential equations by Jacobi wavelet operational matrix

Abstract

In this paper, functions with bounded derivative is considered. Two new estimators E2k,0(f) and E2k,M(f) of functions with bounded derivative have been obtained. These estimators are sharper and best possible. Also, this paper aims to construct a Jacobi wavelet operational matrix based on Jacobi polynomials. The main aim is to solve Riccati differential equation which appears in various fields of science such as Physics and Engineering. This approach is generalization of other wavelet operational matrix methods,e.g., Chebyshev wavelets of first kind, Chebyshev wavelets of second kind, Legendre wavelets, Gegenbauer wavelets, etc, which are special cases of Jacobi wavelets. The obtained estimators, the solutions of Riccati differential equation and real world problem by Jacobi wavelet operational matrix and its comparison with the exact solution are the significant achievement of this research paper.