A fast-convolution based space–time Chebyshev spectral method for peridynamic models

Abstract Peridynamics is a nonlocal generalization of continuum mechanics theory which addresses discontinuous problems without using partial derivatives and replacing them by an integral operator. As consequence, it finds applications in the framework development evolution fractures damages elastic materials. In this paper we consider one-dimensional nonlinear model peridynamics propose suitable two-dimensional fast-convolution spectral method based on Chebyshev polynomials to solve model. This choice allows us gain same accuracy both space time. We show convergence perform several simulations study performance scheme.