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Numerical solution of Riccati equation using the cubic B-spline scaling functions and Chebyshev cardinal functions. (English) Zbl 1205.65206
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:
65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
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