Standard software based on the collocation method for differential equations, delivers a continuous approximation (called the collocation solution) which augments the high order discrete approximate solution that is provided at mesh points. This continuous approximation is less accurate than the discrete approximation. For ’non-standard’ Volterra integro-differential equations with constant del...

The method of orthogonal collocation for solving boundary value problems in ordinary diierential equation is described, and its relationship to classical nite diierence methods is illustrated. Numerical examples demonstrate the capabilities of software based on orthogonal collocation for analyzing nonlinear diierential equations. A new discretiza-tion method for the solution of elliptic partial...

In this paper, a new collocation method, which is based on Boubaker polynomials, is introduced for the approximate solutions of a class of two-dimensional linear Fredholm integral equationsof the second kind. The properties of two-dimensional Boubaker functions are presented. The fundamental matrices of integration with the collocation points are utilized to reduce the solution of the integral ...

We present Galerkin methods in both the age and space variables for an agedependent population undergoing nonlinear diffusion. The methods presented are a generalization of methods, where the approximation space in age is the space of piecewise constant functions. In this paper, we allow the use of discontinuous piecewise polynomial subspaces of L2 as the approximation space in age. As in the p...

Alocal convergence rate is established for an orthogonal collocationmethod based on Gauss quadrature applied to an unconstrained optimal control problem. If the continuous problem has a smooth solution and the Hamiltonian satisfies a strong convexity condition, then the discrete problem possesses a local minimizer in a neighborhood of the continuous solution, and as the number of collocation po...

We consider the numerical integration of functions with point singularities over a planar wedge S using isoparametric piecewise polynomial interpolation of the function and the wedge. Such integrals often occur in solving boundary integral equations using the collocation method. In order to obtain the same order of convergence as is true with uniform meshes for smooth functions, we introduce an...