For the nonlinear analysis of structures using the well known Newton-Raphson Method, the tangent stiffness matrices of the elements must be constructed in each iteration. Due to the high expense required to find the exact tangent stiffness matrices, researchers have developed novel innovations into the Newton-Raphson method to reduce the cost and time required by the analysis. In this paper, a ...

In this study, a numerical solution of singular nonlinear differential equations, stemming from biology and physiology problems, is proposed. The methodology is based on the shifted Chebyshev polynomials operational matrix of derivative and collocation. To assess the accuracy of the method, five numerical problems, such as the human head, Oxygen diffusion and Bessel differential equation, were ...

in this paper, an iterative method is proposed for solving large general sylvester matrix equation $axb+cxd = e$, where $a in r^{ntimes n}$ , $c in r^{ntimes n}$ , $b in r^{stimes s}$ and  $d in r^{stimes s}$ are given matrices and $x in r^{stimes s}$  is the unknown matrix. we present a global conjugate gradient (gl-cg) algo- rithm for solving linear system of equations with multiple right-han...

in this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. we utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. by using bernstein polynomial basis, the problem is transformed in...

In this paper, we propose and analyze an efficient matrix method based on Bell polynomials for numerically solving nonlinear Fredholm- Volterra integral equations. For this aim, first we calculate operational matrix of integration and product based on Bell polynomials. By using these matrices, nonlinear Fredholm-Volterra integral equations reduce to the system of nonlinear algebraic equations w...

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...

 Let $P(lambda)$ be an $n$-square complex matrix polynomial, and $1 leq k leq n$ be a positive integer. In this paper, some algebraic and geometrical properties of the $k$-numerical range of $P(lambda)$ are investigated. In particular, the relationship between the $k$-numerical range of $P(lambda)$ and the $k$-numerical range of its companion linearization is stated. Moreover, the $k$-numerical...

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 paper presents an approach for solving a nonlinear stochastic differential equations (nsdes) using a new basis functions (nbfs). these functions and their operational matrices areused for representing matrix form of the nbfs. with using this method in combination with the collocation method, the nsdes are reduced a stochastic nonlinear system of equations and unknowns. then, the error anal...