Sheo Kumar

Convergence of quadratures for Cauchy principal value integrals

AbstractQuadrature formulas based on the “practical” abscissasxk=cos(k π/n),k=0(1)n, are obtained for the numerical evaluation of the weighted Cauchy principal value integrals

Contemporary review of techniques for the solution of nonlinear Burgers equation

\mathop {\rlap{--} \smallint }\limits_{ - 1}^1 (1 - x)^\alpha (1 + x)^\beta (f(x))/(x - a)){\rm E}dx,

Vibration Analysis of a Rotating FGM Thermoelastic Axisymmetric Circular Disk Using FEM

where α,β>−1 andaε(−1, 1). An interesting problem concerning these quadrature formulas is their convergence for a suitable class of functions. We establish convergence of these quadrature formulas for the class of functions which are Hölder-continuous on [−1, 1].ZusammenfassungErmittelt werden die auf den “praktischen” Abszissenxk=cos(k π/n),k=0(1)n, basierten Quadraturformeln für die numerische Berechnung von Cauchyschen gewichteten Hauptwerten

Galerkin-least square B-spline approach toward advection-diffusion equation

\mathop {\rlap{--} \smallint }\limits_{ - 1}^1 (1 - x)^\alpha (1 + x)^\beta (f(x))/(x - a)){\rm E}dx,

On modified increment methods of Garey for nonlinear second kind Volterra integral equations

wobei α,β>−1 undaε(−1, 1). Ein interessantes Problem bezüglich dieser Quadraturformeln ist ihre Konvergenz für die Klasse von Funktionen, die auf [−1, 1] Hölder-kontinuierlich sind.

Solution of advection diffusion equation using finite element method

Abstract In the present work, a comprehensive study of advection–diffusion equation is made using B-spline functions. Advection–diffusion equation has many physical applications such as dispersion of dissolved salts in groundwater, spread of pollutants in rivers and streams, water transfer, dispersion of tracers, and flow fast through porous media. Motivation behind the proposed scheme is to present a solution scheme which is easy to understand. Both linear and quadratic B-spline functions have been used in the present work to understand the basic aspect and advantages of the presented scheme. Along with this, some test examples are studied to observe the correctness of the numerical experiments. Finally, different comparisons are made to cross check the results obtained by the given scheme.