Numerical solution of Riccati equation using the cubic B-spline scaling functions and Chebyshev cardinal functions
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.
riccati equation chebyshev cardinal function operational matrix of derivative cubic b-spline function collocation method