Solving the Interval Riccati differential equation by Wavelet operational matrix method

Abstract

Riccati differential equation is an important equation, in many fields of engineering and applied sciences, so recently lots of methods have been proposed to solve this equation. Haar Wavelet operational matrix,is one of the effective methods to solve this equation, that is very simple and easy, compared to other orders. In this paper, we want to solve the nonlinear riccati differential equation in interval initial condition. first we simplify it by using the block pulse function to expand the Haar wavelet one. we have three cases for each interval, but now it can be solved for positive interval Haar coefficients. The results reveal that the proposed method is very effective and simple.