Generalized Gauss – Radau and Gauss – Lobatto Formulae ∗

On Gautschi's conjecture for generalized Gauss-Radau and Gauss-Lobatto formulae

Recently, Gautschi introduced so-called generalized Gauss-Radau and Gauss-Lobatto formulae which are quadrature formulae of Gaussian type involving not only the values but also the derivatives of the function at the endpoints. In the present note we show the positivity of the corresponding weights; this positivity has been conjectured already by Gautschi. As a consequence, we establish several ...

Generalized Gauss-Radau and Gauss-Lobatto formulas with Jacobi weight functions

We derive explicitly the weights and the nodes of the generalized Gauss-Radau and Gauss-Lobatto quadratures with Jacobi weight functions. AMS subject classification: 65D32, 65D30, 41A55.

Applications of Gauss-Radau and Gauss-Lobatto Numerical Integrations Over a Four Node Quadrilateral Finite Element

In this paper Gauss-Radau and Gauss-Lobatto quadrature rules are presented to evaluate the rational integrals of the element matrix for a general quadrilateral. These integrals arise in finite element formulation for second order Partial Differential Equation via Galerkin weighted residual method in closed form. Convergence to the analytical solutions and efficiency are depicted by numerical ex...

Rates of Convergence of Gauss, Lobatto, and Radau Integration Rules for Singular Integrands

Rates of convergence (or divergence) are obtained in the application of Gauss, Lobatto, and Radau integration rules to functions with an algebraic or logarithmic singularity inside, or at an endpoint of, the interval of integration. A typical result is the following: For a generalized Jacobi weight function on [-1,1], the error in applying an «-point rule to f(x) = \x -y\~* isO(n~2 + 2i), if y ...

Gauss-Lobatto Formulae and Extremal Problems with Polynomials