On the Derivation and Analysis of a Highly Eccient Method for the Approximation of Quadratic Riccati Equations
A highly e¢cient method is derived and analyzed in this paper for the approximation of Quadratic Riccati Equations (QREs) using interpolation and collocation procedure. The derivation is carried out within a two-step integration interval. We are motivated to derive a method that approximates QREs (which are nonlinear differential equations that have a great deal of applications in science and engineering). Furthermore, the basic properties of the newly derived method, which include the order of accuracy, convergence, zero-stability, consistence and region of absolute stability were analyzed. The method derived was also applied to solve some QREs and from the results generated, it was clear that the new method performed better than the ones with which we juxtaposed our results with.
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