It is shown that the Kronrod extension to the «-point Gauss integration rule, with respect to the weight function (1 x2)V~"2, 0 < M < 2, ju i= 1, is of exact precision 3n + 1 for n even and 3n + 2 for n odd. Similarly, for the (n-t-l)-point Lobatto rule, with — V¡ < M < 1, u ^ 0, the exact precision is 3n for n odd and 3n + 1 for n even.

We propose and analyze a C spectral element method for a model eigenvalue problem with discontinuous coefficients in the one dimensional setting. A super-geometric rate of convergence is proved for the piecewise constant coefficients case and verified by numerical tests. Furthermore, the asymptotical equivalence between a Gauss-Lobatto collocation method and a spectral Galerkin method is establ...

A general framework is introduced to analyze the approximation properties of mapped Legendre polynomials and of interpolations based on mapped Legendre–Gauss–Lobatto points. Optimal error estimates featuring explicit expressions on the mapping parameters for several popular mappings are derived. These results not only play an important role in numerical analysis of mapped Legendre spectral and ...

We consider the construction of a special family of Runge–Kutta (RK) collocation methods based on intra-step nodal points of Chebyshev–Gauss–Lobatto type, with A-stability and stiffly accurate characteristics. This feature with its inherent implicitness makes them suitable for solving stiff initial-value problems. In fact, the two simplest cases consist in the well-known trapezoidal rule and th...

in the present paper, we develop a modified pseudospectral scheme for solving an optimal control problem which is governed by a switched dynamical system. many real-world processes such as chemical processes, automotive systems and manufacturing processes can be modeled as such systems. for this purpose, we replace the problem with an alternative optimal control problem in which the switching t...

This paper formulates a modified differential quadrature finite element method (DQFEM) by combination of the standard DQFEM and virtual boundary spring technique, which makes it easy to implement arbitrary elastic restraints assigning reasonable values stiffnesses. new formulated can offer unified solution for flexural vibrations composite laminates subjected general combinations including all ...

Nodal point sets, and associated collocation projections, play an important role in a range of high-order methods, including Flux Reconstruction (FR) schemes. Historically, efforts have focused on identifying nodal sets that aim to minimise the L∞ error interpolating polynomial. The present work combines comprehensive review known approximation theory results, with new numerical experiments, mo...

In this paper, we introduce peridynamic theory and its application to Richards’ equation with a piecewise smooth initial condition. Peridynamic is non-local continuum that models the deformation failure of materials. describes unsaturated flow water through porous media, it plays an essential role in many applications, such as groundwater management, soil science, environmental engineering. We ...

We introduce a multiple interval Chebyshev-Gauss-Lobatto spectral collocation method for the initial value problems of the nonlinear ordinary differential equations (ODES). This method is easy to implement and possesses the high order accuracy. In addition, it is very stable and suitable for long time calculations. We also obtain the hp-version bound on the numerical error of the multiple inter...