Multistep algorithm to solve general Riccati differential equations by Walsh polynomials approach

Abstract. In this paper, we aim to introduce a procedure for the numerical solution of initial value problems associated with general Riccati-type differential equations. The core idea of the method is based on the approach developed by György Gát and Rodolfo Toledo, which has been successfully applied to the solution of linear differential equations. Our goal is to provide an iterative method that, starting from the initial point, constructs a Walsh polynomial that approximates the theoretical solution of the problem.