Spherical prism gravity effects by Gauss-Legendre quadrature integration
نویسندگان
چکیده
منابع مشابه
Gauss Legendre-Gauss Jacobi quadrature rules over a tetrahedral region
This paper presents a Gaussian quadrature method for the evaluation of the triple integral ( , , ) T I f x y z d xd yd z = ∫∫∫ , where ) , , ( z y x f is an analytic function in , , x y z and T refers to the standard tetrahedral region:{( , , ) 0 , , 1, 1} x y z x y z x y z ≤ ≤ + + ≤ in three space( , , ). x y z Mathematical transformation from ( , , ) x y z space to ( , , ) u v w space maps th...
متن کاملGauss-Legendre principal value integration
few problems lend themselves to closed-form solution, we often need to convert formal definitions into practical numerical methods. One such problem deals with the Principal Value integral, which many students encounter in a course on functions of a complex variable. However, the prospect of evaluating one numerically might seem rather daunting. To the best of my knowledge, the subject remains ...
متن کاملTwo Point Gauss–legendre Quadrature Rule for Riemann–stieltjes Integrals
In order to approximate the Riemann–Stieltjes integral ∫ b a f (t) dg (t) by 2–point Gaussian quadrature rule, we introduce the quadrature rule ∫ 1 −1 f (t) dg (t) ≈ Af ( − √ 3 3 ) + Bf (√ 3 3 ) , for suitable choice of A and B. Error estimates for this approximation under various assumptions for the functions involved are provided as well.
متن کاملIteration-Free Computation of Gauss-Legendre Quadrature Nodes and Weights
Gauss–Legendre quadrature rules are of considerable theoretical and practical interest because of their role in numerical integration and interpolation. In this paper, a series expansion for the zeros of the Legendre polynomials is constructed. In addition, a series expansion useful for the computation of the Gauss–Legendre weights is derived. Together, these two expansions provide a practical ...
متن کاملPositivity of the Weights of Extended Gauss-Legendre Quadrature Rules
We show that the weights of extended Gauss-Legendre quadrature rules are all positive.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Geophysical Journal International
سال: 2007
ISSN: 0956-540X,1365-246X
DOI: 10.1111/j.1365-246x.2007.03214.x