Matrix functions are used in many areas of linear algebra and arise in numerical applications in science and engineering. In this paper, we introduce an effective approach for determining matrix function f(A)=g(q(A)) of a square matrix A, where q is a polynomial function from a degree of m and also function g can be a transcendental function. Computing a matrix function f(A) will be time- consu...

this article gives an approach to predict the springbackward phenomena during post solidification cooling in a functionally graded hybrid composite cylindrical shell with transverse isotropic structure. here the material properties are considered to be given with a general parabolic power-law function. during theoretical analysis, appropriate transform is introduced in the equilibrium equation ...

The space-time neutron diffusion equations with multi-group of delayed neutrons are a couple of the stiff nonlinear partial differential equations. The finite difference method is used to reduce the partial differential equations into ordinary differential equations. This ordinary differential equations are rewritten in a matrix form. The general solution of the matrix differential equation con...

In a turning process modeled using delay differential equations (DDEs), we investigate the stability of the regenerative machine tool chatter problem. An approach using the matrix Lambert W function for the analytical solution to systems of delay differential equations is applied to this problem and compared with the result obtained using a bifurcation analysis. The Lambert W function, known to...

in this paper, we introduce a family of fractional-order chebyshev functions based on the classical chebyshev polynomials. we calculate and derive the operational matrix of derivative of fractional order $gamma$ in the caputo sense using the fractional-order chebyshev functions. this matrix yields to low computational cost of numerical solution of fractional order differential equations to the ...

in this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional volterra-fredholm integro-differential equations. here, we use the so-called two-dimensional block-pulse functions.first, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. then, by using this matrices, the nonlinear two-dimensional vol...

Special matrix functions appear in the literature related to statistics [1-4] and more recently in connection with matrix analogues of Laguerre, Hermite and Legendre differential equations and the corresponding polynomial families [5-7]. The connection between the Humbert matrix function and modified Bessel matrix function has been established in [8,9]. In recent papers [10,11], we defined and ...

block ciphers have wide applications for hardware and software implementations. in this paper, a new block cipher algorithm with provable security is proposed. the whole structure of the algorithm is novel and has a good encryption and decryption performance. additionally, it has good security with few number of rounds. the structure of the proposed algorithm consists of 4-rounds feistel-like w...

in this article we implement an operational matrix of fractional integration for legendre polynomials. we proposed an algorithm to obtain an approximation solution for fractional differential equations, described in riemann-liouville sense, based on shifted legendre polynomials. this method was applied to solve linear multi-order fractional differential equation with initial conditions, and the...

in this paper, the goursat problem of a general form for a linear partial differential equation is investigated with the help of the riemann function method. some results are given concerning the existence and uniqueness for the solution of the suggested problem.