in this study, the problem of determining an optimal trajectory of a nonlinear injection into orbit problem with minimum time was investigated. the method was based on orthogonal polynomial approximation. this method consists of reducing the optimal control problem to a system of algebraic equations by expanding the state and control vector as chebyshev or legendre polynomials with undetermined...

In this paper, three numerical solutions for the Kortewegde Vries Burgers’ (KdVB) equation are presented. Two of these methods are based on cardinal Chebyshev basis function with Galerkin method. Gauss-quadrature formula and El-gendi method are used to convert the problem into system of ordinary differential equations. In the third proposed method, the cardinal Legendre basis function with Gale...

We show that Chebyshev Polynomials are a practical representation of computable functions on the computable reals. The paper presents error estimates for common operations and demonstrates that Chebyshev Polynomial methods would be more efficient than Taylor Series methods for evaluation of transcendental functions. Keywords—Approximation Theory, Chebyshev Polynomial, Computable Functions, Comp...

We analyze whether a given set of analytic functions is an Extended Chebyshev system. This family of functions appears studying the number of limit cycles bifurcating from some nonlinear vector field in the plane. Our approach is mainly based on the so called Derivation-Division algorithm. We prove that under some natural hypotheses our family is an Extended Chebyshev system and when some of th...