This paper considers the numerical solution of boundary integral equations of the second kind for Laplace s equation u on connected regions D in R with boundary S The boundary S is allowed to be smooth or piecewise smooth and we let f K j K Ng be a triangulation of S The numerical method is collocation with approximations which are piecewise quadratic in the parametrization variables leading to...

Finite element methods and the associate collocation methods are considered for solving first-order hyperbolic systems, positive in the sense of Friedrichs. Applied in the case when the meshes are rectangle, those methods lead for example to the successfully used box scheme for the heat equation or D.S.N. scheme for the neutron transport equation. Generalizations of these methods are described ...

Numerical approximations of fractional PDEs in unbounded domains are considered in this paper. Since their solutions decay slowly with power laws at infinity, a domain truncation approach is not effective as no transparent boundary condition is available. We develop efficient Hermite-collocation and Hermite–Galerkin methods for solving a class of fractional PDEs in unbounded domains directly, a...

In this paper we propose a suitable combination of two collocation methods based on the zeros Jacobi polynomials in order to approximate solution Fredholm integral equations [â??1,1]. One main interesting aspects procedure is that our approach cheaper than usual method standard Lagrange interpolation using zeros. Moreover, can successfully manage functions with algebraic singularities at endpoi...

‎In this paper‎, ‎we study the numerical solution of Convection-Diffusion equation with a memory term subject to initial boundary value conditions‎. ‎Finite difference method in combination with product trapezoidal integration rule is used to discretize the equation in time and sinc collocation method is employed in space‎. ‎The accuracy and error analysis of the method are discussed‎. ‎Numeric...

This paper presents an approach for solving a nonlinear stochastic differential equations (NSDEs) using a new basis functions (NBFs). These functions and their operational matrices are used for representing matrix form of the NBFs. With using this method in combination with the collocation method, the NSDEs are reduced a stochastic nonlinear system of equations and unknowns. Then, the error ana...

Alternative Legendre polynomials (ALPs) are used to approximate the solution of a class of nonlinear Volterra-Hammerstein integral equations. For this purpose, the operational matrices of integration and the product for ALPs are derived. Then, using the collocation method, the considered problem is reduced into a set of nonlinear algebraic equations. The error analysis of the method is given an...

Two discrete-time orthogonal spline collocation schemes are formulated and analyzed for solving the linear time-dependent Schrr odinger equation in two space variables. These are Crank-Nicolson and alternating direction implicit (ADI) schemes employing C 1 piecewise polynomial spaces of arbitrary degree 3 in each space variable. The stability of the schemes is examined and optimal order a prior...

We present a new application of the complex polynomial method variant of the complex variable boundary element method. Instead of fitting the boundary conditions using collocation points, we minimize the error of fit in the l2 norm to minimize the least-squares error. This approach greatly enhances the utility and efficiency of the method, allowing us to apply the method to a variety of enginee...

This paper presents an alternative approach for the computation of trajectory segments on slow manifolds of saddle type. This approach is based on iterative methods rather than collocation-type methods. Compared to collocation methods, which require mesh refinements to ensure uniform convergence with respect to , appropriate estimates are directly attainable using the method of this paper. The ...