Riccati Differential Equations: A Computational Approach

One of the most important classes of nonlinear differential equations that have a great deal of applications is the Riccati Differential Equations (RDEs). In this paper, a quarter-step method is derived for the solution of RDEs by collocating and interpolating the Laguerre polynomial basis function. To establish the reliability and applicability of the method on RDEs, some model problems have been solved. The results obtained in terms of the point wise absolute errors show that the method developed approximates the exact solution closely. The research further investigated the basic properties of the method developed and found it to be zero-stable, consistent and convergent.