Two approaches to a numerical solution of a problem concerning impact on the surface of a solid elastic cylinder

Grid approximations of the pseudospectral type with an improved condition number for second-order differential operators

“…The estimates of [8] are refined and summarized in [9,10]. For some partial differential equations, pseudospectral and spectral methods, as well as questions of their realization were analyzed in [11][12][13][14][15][16][17]. In [7], by means of methods of the theory of approximations, the computational properties of pseudospectral methods for some simple linear ordinary differential equations were studied.…”

“…The finite-difference technique was utilized for studying pseudospectrai methods in [15]. When solving hyperbolic equations numerically, the inaccuracy of the approximation of eigenvalues of the elliptic part plays a principal role in exciting parasitic oscillations [17]. The polynomial spectral and pseudospectral methods (due to Chebyshev, Legendre, Gauss, and Jacobi) utilize the corresponding orthogonal polynomials as a basis, and therefore they are free from this disadvantage.…”