We establish a powerful numerical algorithm to compute solutions of coupled system variable fractional order differential equations. Our numer?ical procedure is based on Bernstein polynomials. The mentioned polynomials are non-orthogonal and have the ability produce good results as compared some other method like wavelet. By differentiation integration, operational matrices formed. On using obt...

This paper presents a simple and computationally-efficient algorithm for solving steady two-dimensional subsonic and transonic compressible flow over an airfoil. This work uses an interactive viscous-inviscid solution by incorporating the viscous effects in a thin shear-layer. Boundary-layer approximation reduces the Navier-Stokes equations to a parabolic set of coupled, non-linear partial diff...

In the present paper, we propose the global full orthogonalization method (Gl-FOM) and global generalized minimum residual (Gl-GMRES) method for solving large and sparse general coupled matrix equations

Time-dependent density matrix functional theory can be formulated in terms of coupled-perturbed response equations, in which a coupling matrix K(omega) features, analogous to the well-known time-dependent density functional theory (TDDFT) case. An adiabatic approximation is needed to solve these equations, but the adiabatic approximation is much more critical since there is not a good "zero ord...

in this paper, an optimal control of quadratic performance index with nonlinear constrained is presented. the sine-cosine wavelet operational matrix of integration and product matrix are introduced and applied to reduce nonlinear differential equations to the nonlinear algebraic equations. then, the newton-raphson method is used for solving these sets of algebraic equations. to present ability ...

in this paper, the numerical technique based on hybrid bernoulli and block-pulse functions has been developed to approximate the solution of system of linear volterra integral equations. system of volterra integral equations arose in many physical problems such as elastodynamic, quasi-static visco-elasticity and magneto-electro-elastic dynamic problems. these functions are formed by the hybridi...

A coupled model based on finite element method (FEM) and scaled boundary finite element method (SBFEM) for transient dynamic response of large-scale SSI systems is presented. The wellestablished FEM is used for modeling the near-field bounded domains. A local high-order transmitting boundary, which is based on SBFEM and the improved continued fraction solution for the dynamic stiffness matrix, ...