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.

This paper is devoted to the numerical comparison of methods applied to solve problems with nonlocal boundary conditions. Four numerical methods are compared, namely, finite differences method, Galerkin method, Keller Box scheme and orthogonal spline collocation method. Mathematics Subject Classification: 74S05, 74S20, 74S30, 74H15

An overlapping domain decomposition, additive Schwarz, conjugate gradient method is presented for the solution of the linear systems which arise when orthogonal spline collocation with piecewise Hermite bicu-bics is applied to the Dirichlet problem for Poisson's equation on a rectangle .

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.

Most mathematical models contain uncertainties that may be originated from various sources such as initial and boundary conditions, geometry representation of the domain and input parameters. When these sources are expressed as random processes or random fields, partial differential equations describing the underlying models become stochastic partial differential equations (SPDEs). Stochastic m...