ON THE APPROXIMATION ALGORITHMS FOR SOLVING RICCATI DIFFERENTIAL EQUATIONS USING PIECEWISE CONSTANT ARGUMENTS METHOD

This paper presents an efficient approach for determining an approximate solution to Riccati differential equations with variable coefficients. The approach is introduced as a differential equation with piecewise constant arguments, corresponding to the considered initial value problem, which depends on a positive integer . It is shown that this equation has a unique piecewise smooth solution, which serves as an approximate solution to the considered initial value problem for large . Numerical results are provided, demonstrating the efficiency and high accuracy of the proposed method.