the current paper proposes a technique for the numerical solution of linear control systems.the method is based on galerkin method, which uses the interpolating scaling functions. fora highly accurate connection between functions and their derivatives, an operational matrix forthe derivatives is established to reduce the problem to a set of algebraic equations. several testproblems are given, a...

in this paper, unsteady two phase simulation of nanofluid flow and heat transfer between moving parallel plates, in presence of the magnetic field is studied. the significant effects of thermophoresis and brownian motion have been contained in the model of nanofluid flow. the three governing equations are solved simultaneously via galerkin method. comparison with other works indicates that this...

surface and small scale effects on free transverse vibration of a single-walled carbon nanotube (swcnt) fitted with y-junction at downstream end conveying viscose fluid is investigated in this article based on euler-bernoulli beam (ebb) model. nonlocal elasticity theory is employed to consider small scale effects due to its simplicity and efficiency. the energy method and hamilton’s principle a...

In this work, we show quasi-optimal interface error estimates for solutions obtained by the symmetric interior penalty discontinuous Galerkin method. It is proved that the numerical solution restricted to an interface converges with order |lnh|h under suitable regularity requirements, where the logarithmic factor is only present in the lowest order case, i.e., k = 1. For this case, we also deri...

We discuss the optimality in L2 of a variant of the Incomplete Discontinuous Galerkin Interior Penalty method (IIPG) for second order linear elliptic problems. We prove optimal estimate, in two and three dimensions, for the lowest order case under suitable regularity assumptions on the data and on the mesh. We also provide numerical evidence, in one dimension, of the necessity of the regularity...

In this paper, a numerical algorithm using a coupled Galerkin-Differential Quadrature (DQ) method is proposed for the solution of dam-reservoir interaction problem. The governing differential equation of motion of the dam structure is discretized by the Galerkin method and the DQM is used to discretize the fluid domain. The resulting systems of ordinary differential equations are then solved by...

a relationship based on the modified couple stress theory is developed to investigate the flexural sensitivity of an atomic force microscope (afm) with assembled cantilever probe (acp). this acp comprises a horizontal cantilever, two vertical extensions and two tips located at the free ends of the extensions which form a caliper. an approximate solution to the flexural vibration problem is obta...

sinc-galerkin method based upon double exponential transformation for solving troesch's problem was given in this study. properties of the sinc-galerkin approach were utilized to reduce the solution of nonlinear two-point boundary value problem to same nonlinear algebraic equations, also, the matrix form of the nonlinear algebraic equations was obtained.the error bound of the method was fo...

Many inequality relations between real vector quantities can be succinctly expressed as “weak (sub)majorization” relations using the symbol ≺w. We explain these ideas and apply them in several areas, angles between subspaces, Ritz values, and graph Laplacian spectra, which we show are all surprisingly related. Let Θ(X ,Y) be the vector of principal angles in nondecreasing order between subspace...

In this paper we introduce a new method for solving partial and ordinary differential equations with large first, second and third derivatives of the solution in some part of the domain using the finite element technique (here called the Galerkin-Gokhman method). The method is based on the application of the Galerkin method to a modified differential equation. The exact solution of the modified...