Powell–Sabin splines are piecewise quadratic polynomials with a global C1-continuity, defined on conforming triangulations. Imposing boundary conditions on such a spline leads to a set of constraints on the spline coefficients. First, we discuss boundary conditions defined on a polygonal domain, before we treat boundary conditions on a general curved domain boundary. We consider Dirichlet and N...

In this paper we introduce a nodal spline collocation method for the numerical solution of Cauchy singular integral equations. Uniform error bounds of the approximate solution are provided and some numerical examples are presented. c © 2008 European Society of Computational Methods in Sciences and Engineering

Abstract In this study, the time-dependent potential coefficient in a higher-order PDE with initial and boundary conditions is numerically constructed for first time from nonlocal integral condition. Even though inverse identification problem investigated study ill-posed, it has unique solution. For discretizing direct finding stable accurate solutions, we employ Quintic B-spline (QBS) collocat...

In this paper, we study polynomial spline collocation methods applied to a particular class of integral-algebraic equations of Volterra type. We analyse mixed systems of second and first kind integral equations. Global convergence and local superconvergence results are established.

This paper proposes a numerical method to obtain an approximation solution for the time-fractional Schrödinger Equation (TFSE) based on combination of cubic trigonometric B-spline collocation and Crank-Nicolson scheme. The fractional derivative operator is described in Caputo sense. L1−approximation used discretization. Using Von Neumann stability analysis, proposed technique shown be condition...

Since the solution of a second-kind Volterra integral equation with weakly singular kernel has, in general, unbounded derivatives at the left endpoint of the interval of integration, its numerical solution by polynomial spline collocation on uniform meshes will lead to poor convergence rates. In this paper we investigate the convergence rates with respect to graded meshes, and we discuss the pr...

In usual boundary elements methods, the mixed Dirichlet-Neumann problem in a plane polygonal domain leads to difficulties because of the transition of spaces in which the problem is well posed. We build collocation methods based on a mixed single and double layer potential. This indirect method is constructed in such a way that strong ellipticity is obtained in high order spaces of Sobolev type...

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...

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...

The aim of this paper is to solve the second order neutral delay differential equations (NDDEs) based on seventh C3-spline collocation methods with three parameters c1, c2, c3 ∈ (0, 1). It is shown that the proposed methods for second order NDDEs possess a convergence rate of order seven if : 1− c1 − c2 − c3 + c1c2 + c1c3 + c2c3 − 2c1c2c3 ≤ 0. Numerical results illustrating the behavior of the ...