Vikash Kumar

Bio: Vikash Kumar is an academic researcher from Madanapalle Institute of Technology and Science. The author has co-authored 1 publications.

Non-symmetric indentation of an elastic half-plane

Abstract: In this work, the problems of wave propagation in a half-space due to the indentation by a rigid wedge at a constant speed and by a parabolic punch at a constant acceleration have been considered separately. The elastodynamics problems of non-symmetric indentation over a contact region expanding at a constant speed and constant acceleration have been solved using the method of homogeneous functions. Following Cherepanov and Cherepanov et al., the general solution of the problems has been derived in terms of an analytic function of complex variables. The expressions for the stress component under the contact region and the torque over the contact region have been derived. Numerical results of the particular cases of the Problems I and III and of the Problems II and IV have been presented in the form of graphs. This work and its applications are expected to be helpful in the study of indentation-related problems of solid mechanics.

The Application of Splines of the Seventh Order Approximation to the Solution of Integral Fredholm Equations

Abstract: There are various numerical methods for solving integral equations. Among the new numerical methods, methods based on splines and spline wavelets should be noted. Local interpolation splines of a low order of approximation have proved themselves well in solving differential and integral equations. In this paper, we consider the construction of a numerical solution to the Fredholm integral equation of the second kind using spline approximations of the seventh order of approximation. The support of the basis spline of the seventh order of approximation occupies seven grid intervals. We apply various modifications of the basis splines of the seventh order of approximation at the beginning, the middle, and at the end of the integration interval. It is assumed that the solution of the integral equation is sufficiently smooth. The advantages of using splines of the seventh order of approximation include the use of a small number of grid nodes to achieve the required error of approximation. Numerical examples of the application of spline approximations of the seventh order for solving integral equations are given.

Application of Splines of the Seventh Order Approximation to the Solution of the Fredholm Integral Equations with Weekly Singularity

Abstract: We consider the construction of a numerical solution to the Fredholm integral equation of the second kind with weekly singularity using polynomial spline approximations of the seventh order of approximation. The support of the basis spline of the seventh order of approximation occupies seven grid intervals. In the beginning, in the middle, and at the end of the integration interval, we apply various modifications of the basis splines of the seventh order of approximation. We use the Gaussian-type quadrature formulas to calculate the integrals with a weakly singularity. It is assumed that the solution of the integral equation is sufficiently smooth. The advantages of using splines of the seventh order of approximation include the use of a small number of grid nodes to achieve the required error of approximation. Numerical examples of the application of spline approximations of the seventh order to solve integral equations are given.