In this paper, we studied the numerical solution of nonlinear weakly singular Volterra-Fredholm integral equations by using the product integration method. Also, we shall study the convergence behavior of a fully discrete version of a product integration method for numerical solution of the nonlinear Volterra-Fredholm integral equations. The reliability and efficiency of the proposed scheme are...

In this article the author constructs an eeective diierence scheme for the solution of coupled dynamic electroelasticity problems for nite dimensional solids. Such a construction is based on the energy conservation law for the electromechanical system and the deenition of generalised solutions for the corresponding diierential problem. Results of computational experiments are presented for holl...

The genus statistics is studied using large N -body simulations for several cosmological models. We consider the e ects of nonlinear gravitational evolution, smoothing the particle data in fully nonlinear regime, and the redshift-space distortion on the genus curve. Detailed comparison between the theoretical prediction in weakly nonlinear theory and the appropriate simulation results shows tha...

We prove short-time existence of smooth solutions for a class of nonlinear, and generally spatially nonlocal, Hamiltonian evolution equations that describe the self-interaction of weakly nonlinear scale-invariant waves. These equations include ones that describe weakly nonlinear hyperbolic surface waves, such as nonlinear Rayleigh waves in elasticity.