In this paper, a new efficient and practical modification of the Adomian decomposition method is proposed with Laguerre polynomials second kind Chebyshev which has not been introduced in other articles to best our knowledge. This approach can be utilized approximately solve linear nonlinear differential equations. The formulations are examined by representative example numerical results confirm...

A novel method for solving optimal tracking control of linear quadratic time-varying systems with differentforms time delays in state and input variables constraints is presented this paper. Using the concepts two powerful wavelets, Legendre Chebyshev we convert problem to a static optimization one. The general from by which one can utilize it other wavelets. proposed has ability solve problems...

In this paper, we propose a method to approximate the solution of a linear Fredholm integro-differential equation by using the Chebyshev wavelet of the first kind as basis. For this purpose, we introduce the first Chebyshev operational matrix of integration. Chebyshev wavelet approximating method is then utilized to reduce the integro-differential equation to a system of algebraic equations. Il...

In a recent article, the first and second kinds of multivariate Chebyshev polynomials fractional degree, relevant integral repesentations, have been studied. this we introduce pseudo-Lucas functions show possible applications these new functions. For kind, compute Newton sum rules any orthogonal polynomial set starting from entries Jacobi matrix. representation formulas for powers r×r matrix, a...

in this paper, we use the continuous legendre wavelets on the interval [0,1] constructed by razzaghi m. and yousefi s. [6] to solve the linear second kind integral equations. we use quadrature formula for the calculation of the products of any functions, which are required in the approximation for the integral equations. then we reduced the integral equation to the solution of linear algebraic ...

Abstract Two efficient quadrature formulae have been developed for evaluating numerically certain singular integral equations of the first kind over the finite interval [-1,1]. Central to this work is the application of four special cases of the Jacobi polynomials P n (x), whose zeros served as interpolation and collocation nodes: (i) α = β = −2 , Tn(x), the first kind Chebyshev polynomials (ii...