LAUSR

In the presented study, we are presenting the approximate solutions of two important equations, the Riccati and Logistic equations; the presented technique is based on the rational Legendre function. Since all the studied models are nonlinear, we convert these nonlinear equations to a sequence of linear ordinary differential equations (ODEs), then by applying the quasi-linearization method (QLM) on these resulting ODEs at each iteration, these ODEs will be converted to a simple linear system of algebraic equations which can be solved. Two numerical examples are presented and we compared between the approximate and the exact solutions.