This work is to provide general spectral and pseudo-spectral Jacobi-PetrovGalerkin approaches for the second kind Volterra integro-differential equations. The Gauss-Legendre quadrature formula is used to approximate the integral operator and the inner product based on the Jacobi weight is implemented in the weak formulation in the numerical implementation. For some spectral and pseudo-spectral ...

Abstract. The main contribution of the current paper is to propose a new effective numerical method for solving the first-order linear matrix differential equations. Properties of the Legendre basis operational matrix of integration together with a collocation method are applied to reduce the problem to a coupled linear matrix equations. Afterwards, an iterative algorithm is examined for solvin...

This paper gives an ecient numerical method for solving the nonlinear systemof Volterra-Fredholm integral equations. A Legendre-spectral method based onthe Legendre integration Gauss points and Lagrange interpolation is proposedto convert the nonlinear integral equations to a nonlinear system of equationswhere the solution leads to the values of unknown functions at collocationpoints.

Supercapacitor is a promising solution to storage of pulsed energy generated by MEMS harvesting systems, relying on its faster charging/discharging capability than secondary battery. To improve the density on-chip supercapacitor which shows potential for integration with devices, in this paper we first present successful electrode design high specific pseudo-supercapacitors basis deep reactive ...

For a weakly pseudo-Hermitian linear operator, we give a spectral condition that ensures its pseudo-Hermiticity. This condition is always satisfied whenever the operator acts in a finite-dimensional Hilbert space. Hence weak pseudo-Hermiticity and pseudo-Hermiticity are equivalent in finite-dimensions. This equivalence extends to a much larger class of operators. Quantum systems whose Hamiltoni...

Local polynomial smoother (LPS) is a weighted local least-squares nonparametric method. It provides a local Taylor series fit of the data at any location and can be directly used in a differential equation to provide a numerical scheme. In this article, we introduce this new nonparametric idea based on local polynomial smoother, for acquiring the numerical solution of the Bagley-Torvik fraction...

In many calculations, spectral discretization in space is coupled with a standard ordinary differential equation formula in time. To analyze the stability of such a combination, one would like simply to test whether the eigenvalues of the spatial discretization operator (appropriately scaled by the time step k) lie in the stability region for the o.d.e. formula, but it is well known that this k...

Stiffness matrix of the four-node quadrilateral plane stress element is decomposed into normal and shear components. A computer program is developed to obtain the straining modes using adequate and reduced integration. Then a solution for the problem of mixing straining modes is found. Accuracy of the computer program is validated by a closed-form stiffness matrix, derived for the plane rectang...

INTRODUCTION Flows involving two phases can be found in many industrial applications. Models that can accurately predict the behaviour of these ows in complex physical situations such as turbulent ow with rotation, and unsteady turbulent two-phase ows, are lacking. Numerical simulation of the detailed behaviour of the drops or bubbles in a complex and unsteady turbulent ow can provide a fundame...

We consider the max-plus analogue of the eigenproblem for matrix pencils, A ⊗ x = λ⊗ B ⊗ x. We show that the spectrum of (A, B) (i.e., the set of possible values of λ), which is a finite union of intervals, can be computed in pseudopolynomial number of operations, by a (pseudo-polynomial) number of calls to an oracle that computes the value of a mean payoff game. The proof relies on the introdu...