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Zbl 1205.65206
Lakestani, Mehrdad; Dehghan, Mehdi
Numerical solution of Riccati equation using the cubic B-spline scaling functions and Chebyshev cardinal functions. (English)
[J] Comput. Phys. Commun. 181, No. 5, 957-966 (2010). ISSN 0010-4655

Summary: Two numerical techniques are presented for solving the solution of Riccati differential equation. These methods use the cubic B-spline scaling functions and Chebyshev cardinal functions. The methods consist of expanding the required approximate solution as the elements of cubic B-spline scaling function or Chebyshev cardinal functions. Using the operational matrix of derivative, we reduce the problem to a set of algebraic equations. Some numerical examples are included to demonstrate the validity and applicability of the new techniques. The methods are easy to implement and produce very accurate results.

MSC 2000:: *65L05 Initial value problems for ODE (numerical methods)
34A34 Nonlinear ODE and systems, general
65L60 Finite numerical methods for ODE

Keywords: cubic B-spline function; Riccati equation; Chebyshev cardinal function; collocation method; operational matrix of derivative; numerical examples

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