A new moving mesh method is introduced for solving time dependent partial diierential equations (PDEs) in divergence form. The method uses a cell-averaging cubic Hermite collocation discretization for the physical PDEs and a three point nite diierence discretization for the PDE which determines the moving mesh. Numerical results are presented for a selection of diicult benchmark problems, inclu...

The Meshless Local Petrov-Galerkin (MLPG) mixed collocation method is proposed in this paper, for solving elasticity problems. In the present MLPG approach, the mixed scheme is applied to interpolate the displacements and stresses independently, as in the MLPG finite volume method. To improve the efficiency, the local weak form is established at the nodal points, for the stresses, by using the ...

Recently, there has been an increasing interest in the study of singular and perturbed systems. In this paper we propose a collocation method for solving singularly perturbed Volterra integro-differential and Volterra integral equations. The method is based upon radial basis functions, using zeros of the shifted Legendre polynomial as the collocation points. The results of numerical experiments...

In this paper, for analyses of metal forming problems, a point collocation method (PCM) with a boundary layer of finite element is developed. PCMs have some advantages such as no mesh, no integration. While, the robustness of the PCMs is an issue especially when scattered and random points are used. To improve the robustness, some studies suggest that the positivity conditions can be important ...

We reveal the relationship between a Petrov–Galerkin method and a spectral collocation method at the Chebyshev points of the second kind (±1 and zeros of Uk) for the two-point boundary value problem. Derivative superconvergence points are identified as the Chebyshev points of the first kind (Zeros of Tk). Super-geometric convergent rate is established for a special class of solutions.

We have suggested the numerical schemes of collocation methods and mechanical quadrature methods for approximative solution of singular integro-differential equations with kernels of Cauchy type. The equations are defined on the arbitrary smooth closed contours of complex plane. The researched methods are based on the descritization by Fejér points. Theoretical background for collocation method...

A new algorithm for solving the general nonlinear third-order differential equation is developed by means of a shifted Jacobi-Gauss collocation spectral method. The shifted Jacobi-Gauss points are used as collocation nodes. Numerical examples are included to demonstrate the validity and applicability of the proposed algorithm, and some comparisons are made with the existing results. The method ...

We examine a class of symmetric collocation schemes for the solution of nonlinear boundary value problems for unstructured nonlinear systems of differential-algebraic equations with arbitrary index. We show that these schemes converge with the same orders as one would expect for ordinary differential equations. In particular, we show superconvergence for a special choice of the collocation poin...

We analyze a least-squares strong-form kernel collocation formulation for solving second order elliptic PDEs on smooth, connected and compact surfaces with bounded geometry. The methods do not require any partial derivatives of surface normal vectors or metric. Based on some standard smoothness assumptions for high order convergence, we provide the sufficient denseness conditions on the colloca...

A collocation-Galerkin scheme is proposed for an initial-boundary value problem for a first order hyperbolic equation in one space dimension. The Galerkin equations satisfied by the approximating solution are obtained from a weak-weak formulation of the initial-boundary value problem. The collocation points are taken to be affine images of the roots of the Jacobian polynomials of degree r — \ o...