A Mixed Quadrature Rule Using Birkhoff-Young Rule Through Richardson Extrapolation for Numerical Integration of Analytic Functions | Chapter 4 | Research Updates in Mathematics and Computer Science Vol. 2

 This study introduces a novel high-precision quadrature rule, achieved by using two lower-precision quadrature rules. The focus is on facilitating the approximate evaluation of integrals over line segments in the complex plane, particularly for analytic functions. The versatility of the newly developed quadrature rule is demonstrated through its application to various mathematical scenarios. To assess the efficacy of the proposed quadrature rule, an asymptotic error estimate is provided. Numerical verification is then conducted to validate the accuracy and efficiency of the rule. The results from these numerical experiments highlight the superior precision of our quadrature rule when applied to the numerical integration of functions over complex line segments. This study significantly contributes to the advancement of numerical integration techniques, presenting a promising avenue for achieving heightened accuracy in the evaluation of integrals over complex domains, particularly in the context of analytic functions.

Author(s) Details:

Sanjit Kumar Mohanty,
Department of Mathematics, B.S. College, Jajpur, Odisha-754296, India.

Please see the link here: https://stm.bookpi.org/RUMCS-V2/article/view/13943

Light Deviation around a Spherical Rotating Black Hole to Fifth Order: Lindstedt-Poincar´e and Pad´e Approximations| Chapter 2 | New Frontiers in Physical Science Research Vol. 6

 Light change about a rotating abyss to Fifth Order is planned utilizing the Kerr metric for two together limited and large change angles allowing for possibility various spin values (taking everything in mind direct and reverting orbits , that is co-rotating or counterrotating orbits). For limited angles the Lindstedt-Poincar´e means is working to get well-behaved resolutions, in addition to Pad´e approximants, then we show that the concluding produces wonderful results distinguished to the numerical answers, so trying to be a practicable design for solving this somewhat equatings. Our judgment methods produce more correct results distinguished to second and triennial order calculations that perform in the article. Additionally, the earlier are applied to the supermassive OJ 287 and SgrA* evil dents considering various impact limits. For big deviation angles mathematical unification has existed used.

Author(s) Details:

Pablo Ruales,
Department of Physics, Universidad San Francisco de Quito, Diego de Robles y Via Interoceanica, Ecuador.

Carlos Marin,
Department of Physics, Universidad San Francisco de Quito, Diego de Robles y Via Interoceanica, Ecuador.

Please see the link here: https://stm.bookpi.org/NFPSR-V6/article/view/9208

Generalized Ostrowski Type Inequality with Applications in Numerical Integration, Probability Theory and Special Means| Chapter 8 | Current Topics on Mathematics and Computer Science Vol. 9

For differentiable functions up to second order, whose second order derivatives are limited and first order derivatives are absolutely continuous, a generalisation of the Ostrowski type inequality is described with applications in numerical integration, probability theory, and special means.

Author (S) Details

Nazia Irshad

Department of Mathematics, Dawood University of Engineering and Technology, M. A. Jinnah Road, Karachi-74800, Pakistan.

Asif R. Khan

Department of Mathematics, University of Karachi, University Road, Karachi-75270, Pakistan.

Muhammad Awais Shaikh

Department of Mathematics, Nabi Bagh Z. M. Degree Science College, Saddar, Karachi-74400, Pakistan.

View Book :- https://stm.bookpi.org/CTMCS-V9/article/view/3640