A nonlinear Dirichlet boundary value problem is approximated by an orthogonal spline collocation scheme using piecewise Hermite bicubic functions. Existence, local uniqueness, and error analysis of the collocation solution and convergence of Newton’s method are studied. The mesh independence principle for the collocation problem is proved and used to develop an efficient multilevel solution met...

The variation in the accuracy of the calculated natural frequencies of pre-twisted beams solved with spline collocation method is investigated in this study. The spline collocation method is used to formulate the eigenvalue problems of pre-twisted beams. Three types of boundary conditions are considered. Numerical results indicate that the accuracy of the calculated natural frequencies is signi...

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...

In this paper, we propose a method for translating a given verb-noun collocation based on a parallel corpus and an additional monolingual corpus. Our approach involves two models to generate collocation translations. The combination translation model generates combined translations of the collocate and the base word, and filters translations by a target language model from a monolingual corpus,...

We study the computation of the orthogonal spline collocation solution of a linear Dirichlet boundary value problem with a nonselfadjoint or an indefinite operator of the form Lu = ∑ aij(x)uxixj + ∑ bi(x)uxi + c(x)u. We apply a preconditioned conjugate gradient method to the normal system of collocation equations with a preconditioner associated with a separable operator, and prove that the res...

Time domain boundary integral formulations of transient scattering problems involve retarded potential integral equations. Solving such equations numerically is both complicated and computationally intensive, and numerical methods often prove to be unstable. Collocation schemes are easier to implement than full finite element formulations, but little appears to be known about their stability an...

For solving electroencephalographic forward problem, coupled method of finite element method FEM and fast moving least square reproducing kernel method FMLSRKM which is a kind of meshfree method is proposed. Current source modeling for FEM is complicated, so source region is analyzed usingmeshfreemethod. First order of shape function is used for FEM and second order for FMLSRKM because FMLSRKM ...

We propose and analyze the spectral collocation approximation for the partial integrodifferential equations with a weakly singular kernel. The space discretization is based on the pseudo-spectral method, which is a collocation method at the Gauss-Lobatto quadrature points. We prove unconditional stability and obtain the optimal error bounds which depend on the time step, the degree of polynomia...

Macroscopically heterogeneous materials, characterised mostly by comparable heterogeneity lengthscale and structural sizes, can no longer be modelled by deterministic approach instead. It is convenient to introduce stochastic approach with uncertain material parameters quantified as random fields and/or random variables. The present contribution is devoted to propagation of these uncertainties ...

This work proposes and analyzes a Smolyak-type sparse grid stochastic collocation method for the approximation of statistical quantities related to the solution of partial differential equations with random coefficients and forcing terms (input data of the model). To compute solution statistics, the sparse grid stochastic collocation method uses approximate solutions, produced here by finite el...