A composite Chebyshev finite difference method for nonlinear optimal control problems

Direct solution of nonlinear constrained quadratic optimal control problems using B-spline functions

“…The approximate solutions of x 1 (t), x 2 (t), and u(t), obtained by the B-spline functions with M = 8, and the exact solutions together error bounds |x * 1 (t)−x 1 (t)|, |x * 2 (t)−x 2 (t)| and |u * (t)−u(t)| are plotted in Figure 2. This results show that accuracy of our method in comparison with ChFD scheme [16] whose result are plotted in Figure 3. Fig.…”

Multiple stage satellite launch vehicle ascent optimization using Chebyshev wavelets

“…The proposed method is based on Chebyshev wavelets approximation. Marzban and Hoseini [17] also investigated a composite Chebyshev finite difference method for solving nonlinear optimal control problems. The method was based on BPFs and Chebyshev polynomials using the well-known Chebyshev-Gauss-Lobatto points.…”

“…The second one uses sets of orthogonal polynomials such as Laguerre, Legendre, Chebyshev, etc. The third one consists of sine-cosine functions in Fourier series [17]. One of the most attractive proposals made in the last years is an idea connected to the application of wavelets as the basic functions in the numerical problems.…”

“…Depending on the structure, the orthogonal functions may be widely classified into three families [17]. The first one includes sets of piecewise constant basis functions (PCBFs) such as Walsh, block-pulse, etc.…”

Efficient Spectral Collocation Algorithm for a Two-Sided Space Fractional Boussinesq Equation with Non-local Conditions

“…The main advantage of spectral numerical methods over finite element and finite difference [38][39][40][41][42] methods is its efficiency in achieving a high level of accuracy. Other words,spectral methods have exponential rate of convergence, while the finite difference and finite element schemes have algebraic ones.…”