In this paper, numerical solution of first-order systems of ordinary differential equations (ODEs) is considered and an error estimation method is proposed. By this method, the efficiency of pseudospectral method to solve the systems is determined and a modified pseudospectral method is presented. Furthermore, with providing some examples, the aforementioned cases are dealt with numerically. 20...

In [E. Babolian, M.M. Hosseini, Reducing index, and pseudospectral methods for differential-algebraic equations, Appl. Math. Comput. 140 (2003) 77–90], numerical solution of linear differential-algebraic equations (DAEs) has been presented by pseudospectral method. In this paper, a new error estimation technique is proposed to pseudospectral method such that is well done for linear semi-explici...

In a previous paper we have presented a new method of imposing boundary conditions in the pseudospectral Chebyshev approximation of a scalar hyperbolic equation. The novel idea of the new method is to collocate the equation at the boundary points as well as in the inner grid points, using the boundary conditions as penalty terms. In this paper we extend the above boundary treatment to the case ...

We present a study of the local discontinuous Galerkin method for transient convection-di usion problems in one dimension. We show that p degree piecewise polynomial discontinuous nite element solutions of convection-dominated problems are O( xp+2) superconvergent at Radau points. For di usion-dominated problems, the solution's derivative is O( xp+2) superconvergent at the roots of the derivati...

In this paper, we investigate a new pseudospectral method for mixed boundary value problems defined on quadrilaterals. We introduce a new Legendre-Gauss type interpolation and establish the basic approximation results, which play important roles in pseudospectral method for partial differential equations defined on quadrilaterals. We propose pseudospectral method for two model problems and prov...

Abstract. A local convergence rate is established for an orthogonal collocation method based on Radau quadrature applied to an unconstrained optimal control problem. If the continuous problem has a sufficiently 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...

We propose a numerical method for solving nonlinear initial-value problems of Lane-Emden type. The method is based upon nonclassical Gauss-Radau collocation points, and weighted interpolation. Nonclassical orthogonal polynomials, nonclassical Radau points and weighted interpolation are introduced on arbitrary intervals. Then they are utilized to reduce the computation of nonlinear initial-value...

When finite-difference methods are used to solve the elastic wave equation in a discontinuous medium, the error has two dominant components. Dispersive errors lead to artificial wave trains. Errors from interfaces lead to circular wavefronts emanating from each location where the interface appears *‘jagged” to the rectangular grid. The pseudospectral method can be viewed as the limit of finite ...

An orthogonal system of rational functions is introduced. Some results on rational approximations based on various orthogonal projections and interpolations are established. These results form the mathematical foundation of the related spectral method and pseudospectral method for solving differential equations on the half line. The error estimates of the rational spectral method and rational p...