in this paper, an effective direct method to determine the numerical solution of linear and nonlinear fredholm and volterra integral and integro-differential equations is proposed. the method is based on expanding the required approximate solution as the elements of chebyshev cardinal functions. the operational matrices for the integration and product of the chebyshev cardinal functions are des...

In this work, we employed the Laplace transform of right-sided distributions in conjunction with power series method to obtain distributional solutions modified Bessel equation and its related equation, whose coefficients contain parameters ν γ. We demonstrated that can be expressed as finite linear combinations Dirac delta function derivatives, specific form depending on values

Abstract The principal aim of the current article is to establish new formulas Chebyshev polynomials sixth-kind. Two different approaches are followed derive connection between these and some other orthogonal polynomials. coefficients expressed in terms terminating hypergeometric functions certain arguments; however, they can be reduced cases. New moment sixth-kind also established, virtue such...

Among the simplest of the classical polynomials are the Chebyshev polynomials of the first and second kind, Tk(x) and Uk(x). In our normalization, the indices are allowed to be halfintegers as well as integers, and the “polynomials” actually live in Z[x, √ 2− x, √ 2 + x]. We will show that the rational functions Tm/2(x) Tn/2(x) and Um/2(x) Un/2(x) are very remarkable from the point of view of G...

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...