Modified Gauss-Legendre, Lobatto and Radau cubature formulas for the numerical evaluation of 2-D singular integrals
نویسندگان
چکیده
منابع مشابه
Generalized Gauss – Radau and Gauss – Lobatto Formulae ∗
Computational methods are developed for generating Gauss-type quadrature formulae having nodes of arbitrary multiplicity at one or both end points of the interval of integration. Positivity properties of the boundary weights are investigated numerically, and related conjectures are formulated. Applications are made to moment-preserving spline approximation. AMS subject classification: 65D30.
متن کاملGeneralized 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.
متن کاملRates 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 ...
متن کاملApplications 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...
متن کاملOn 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 ...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 1983
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171283000526