Bernstein Polynomial Multiwavelets Operational Matrix for Solution of Differential Equation

Abstract

A new application of the Bernstein polynomials based multiwavelets approach for the numerical solution of differential equations is given. In the proposed method, Bernstein polynomial multiwavelets are obtained by using orthonormality of Bernstein polynomials. We present the operational matrix of integration of Bernstein polynomial based multiwavelets basis which diminishes the taken differential equation into the system of algebraic equations for less demanding calculations. High accuracy of these results even in the case of a small number of polynomials is observed. The convergence and exactness are described by comparing the ascertained approximated solution and the known analytical solution. The error estimates of the approximate solution are given and also some comparative examples with figures are given to confirm the reliability and accuracy of the proposed method. Some physical problems that lead to the differential equations are examined by the proposed method.