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...

1. Introduction. In this chapter, we give an overview on methods to compute functions of a (usually square) matrix A with particular emphasis on the matrix exponential and the matrix sign function. We will distinguish between methods which indeed compute the entire matrix function, i.e. they compute a matrix, and those which compute the action of the matrix function on a vector. The latter task...

Solving large-scale algebraic Riccati equations (AREs) is one of the central tasks in solving optimal control problems for linear and, using receding-horizon techniques, also nonlinear instationary partial differential equations. Large-scale AREs also occur in several model reduction methods for dynamical systems. Due to sparsity and large dimensions of the resulting coefficient matrices, stand...

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...

we consider an approximation scheme using haar wavelets for solving a class of infinite horizon optimal control problems (ocp's) of nonlinear interconnected large-scale dynamic systems. a computational method based on haar wavelets in the time-domain is proposed for solving the optimal control problem. haar wavelets integral operational matrix and direct collocation method are utilized to ...

in this paper rationalized haar (rh) functions method is applied to approximate the numerical solution of the fractional volterra integro-differential equations (fvides). the fractional derivatives are described in caputo sense. the properties of rh functions are presented, and the operational matrix of the fractional integration together with the product operational matrix are used to reduce t...