A new explicit formula for the integrals of Bernstein polynomials of any degree for any order in terms of Bernstein polynomials themselves is derived. A fast and accurate algorithm is developed for the solution of high even-order boundary value problems (BVPs) with two point boundary conditions but by considering their integrated forms. The Bernstein–Petrov–Galerkinmethod (BPG) is applied to co...

in this paper, we use petrov-galerkin elements such as continuous and discontinuous lagrange-type k-0 elements and hermite-type 3-1 elements to find an approximate solution for linear fredholm integro-differential equations on $[0,1]$. also we show the efficiency of this method by some numerical examples

We extend the Chebyshev-Legendre spectral method to multi-domain case for solving the two-dimensional vorticity equations. The schemes are formulated in Legendre-Galerkinmethod while the nonlinear term is collocated at Chebyshev-Gauss collocation points. We introduce proper basis functions in order that the matrix of algebraic system is sparse. The algorithm can be implemented efficiently and i...

‎In this paper, we discuss about existence of solution for integro-differential system and then we solve it  by using the Petrov-Galerkin method. In the Petrov-Galerkin method choosing the trial and test space is important, so we use Alpert multi-wavelet as basis functions for these spaces. Orthonormality is one of the properties of Alpert multi-wavelet which helps us to reduce computations in ...

This paper deals with the finite element solution of the convection diffusion equation in one and two dimensions. Two main techniques are adopted and compared. The first one includes Petrov-Galerkin based on Lagrangian tensor product elements in conjunction with streamlined upwinding. The second approach represents Bubnov/Petrov-Galerkin schemes based on a new group of exponential elements. It ...

 Abstract: There are some methods for solving integro-differential equations. In this work, we solve the general-order Feredholm integro-differential equations. The Petrov-Galerkin method by considering Chebyshev multiwavelet basis is used. By using the orthonormality property of basis elements in discretizing the equation, we can reduce an equation to a linear system with small dimension. For ...

A new Petrov-Galerkin approach for dealing with sharp or abrupt field changes in Discontinuous Galerkin (DG) reduced order modelling (ROM) is outlined in this paper. This method presents a natural and easy way to introduce a diffusion term into ROM without tuning/optimising and provides appropriate modeling and stablisation for the numerical solution of high order nonlinear PDEs. The approach i...

We study the switching process in chalcogenide superlattice (CSL) phase-change memory materials by describing the motion of an atomic layer between the low and high resistance states. Two models have been proposed by different groups based on high-resolution electron microscope images. Model 1 proposes a transition from Ferro to Inverted Petrov state. Model 2 proposes a switch between Petrov an...

We present a hybridized discontinuous Petrov–Galerkin (HDPG) method for the numerical solution of steady and time-dependent scalar conservation laws. The method combines a hybridization technique with a local Petrov–Galerkin approach in which the test functions are computed to maximize the inf-sup condition. Since the Petrov–Galerkin approach does not guarantee a conservative solution, we propo...

A coordinate-free approach to limits of spacetimes is developed. The limits of the Schwarzschild metric as the mass parameter tends to 0 or ∞ are studied, extending previous results. Besides the known Petrov type D and 0 limits, three vacuum plane-wave solutions of Petrov type N are found to be limits of the Schwarzschild spacetime. pacs numbers: 04.20.Jb, 04.20.Cv