Applications of Composite Numerical Integrations Using Gauss-Radau and Gauss-Lobatto Quadrature Rules
نویسندگان
چکیده
منابع مشابه
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...
متن کاملGeneralized 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.
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A form of Gauss-Quadrature rule over [0,1] has been investigated that involves the derivative of the integrand at the pre-assigned left or right end node. This situation arises when the underlying polynomials are orthogonal with respect to the weight function (): 1 x x ω = − over [0,1]. Along the lines of Golub's work, the nodes and weights of the quadrature rule are computed from a Jacobi-type...
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 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: Journal of Scientific Research
سال: 2010
ISSN: 2070-0245,2070-0237
DOI: 10.3329/jsr.v2i3.5123