We propose a preconditioning method for linear systems of equations arising from piecewise Hermite bicubic collocation applied to twodimensional elliptic PDEs with mixed boundary conditions. We construct an efficient, parallel preconditioner for the GMRES method. The main contribution of the paper is a novel interface preconditioner derived in the framework of substructuring and employing a loc...

In this paper, we provide an analysis on the collocation methods(CM), which uses a large scale of admissible functions such as orthogonal polynomials, trigonometric functions, radial basis functions and particular solutions, etc. The admissible functions can be chosen to be piecewise, i.e., different functions are used in different subdomains. The key idea is that the collocation method can be ...

We extend the piecewise orthogonal collocation method to computing periodic solutions of coupled renewal and delay differential equations. Through a rigorous error analysis, we prove convergence relevant finite-element provide theoretical estimate error. conclude with some numerical experiments further support results.

Abstract: In this paper, we investigate piecewise approximate solution for linear two dimensional Volterra integral equation, based on the interval approximation of the true solution by truncated Chebyshev series. By discretization respect to spatial and time variables, the solution is approximated by using collocation method. Analysis of discretization error is discussed and efficiency of the ...

This paper is concerned with error estimates for the numerical solution of linear ordinary differential equations by global or piecewise polynomial collocation which are based on consideration of the differential operator involved and related matrices and on the residual. It is shown that a significant advantage may be obtained by considering the form of the residual rather than just its norm.

We consider a spline difference scheme on a piecewise uniform Shishkin mesh for a singularly perturbed boundary value problem with two parameters. We show that the discrete minimum principle holds for a suitably chosen collocation points. Furthermore, bounds on the discrete counterparts of the layer functions are given. Numerical results indicate uniform convergence. AMS Mathematics Subject Cla...

A complete stability and convergence analysis is given for twoand three-level, piecewise Hermite bicubic orthogonal spline collocation, Laplacemodified and alternating-direction schemes for the approximate solution of linear parabolic problems on rectangles. It is shown that the schemes are unconditionally stable and of optimal-order accuracy in space and time.