Shifted Legendre method for solutions of Riccati type functional differential equations and application of RL circuit model

Abstract

In order to solve the Riccati type functional differential equations under mixed condition, this research suggests a collocation approach based on shifted Legendre polynomials. These equations are seen in physics and electronic sciences. By means of the evenly spaced collocation points, the shifted Legendre polynomials, their derivatives and matrix forms, the method is constructed. It reduces the problem into a system nonlinear algebraic equations. Error analysis is made. The method is applied to numerical examples and their results are compared with other methods from literature. And also, the method is applied to nonlinear RL electrical circuit model. The results show that the method is effective.