Second-Order Finite Element Approximations and a posteriori Error Estimation for Two-Dimensional Parabolic Systems.
Singularly Perturbed Finite Element Methods.
Small Potential Corrections for the Discrete Eigenvalues of the Sturm-Liouville Problem.
Solution of an extraordinary differential equation by Adomian decomposition method.
Some properties of the discontinuous Galerkin method for one-dimensional singularly perturbed problems.
Some results about the pseudospectral approximation of one-dimensional fourth-order problems.
Special exact curved finite elements
Special exact curved finite elements useful for solving contact problems of the second order in domains boundaries of which consist of a finite number of circular ares and a finite number of line segments are introduced and the interpolation estimates are proved.
Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit
In this paper we introduce numerical schemes for a one-dimensional kinetic model of the Boltzmann equation with dissipative collisions and variable coefficient of restitution. In particular, we study the numerical passage of the Boltzmann equation with singular kernel to nonlinear friction equations in the so-called quasi elastic limit. To this aim we introduce a Fourier spectral method for the Boltzmann equation [25, 26] and show that the kernel modes that define the spectral method have the correct...
Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit
In this paper we introduce numerical schemes for a one-dimensional kinetic model of the Boltzmann equation with dissipative collisions and variable coefficient of restitution. In particular, we study the numerical passage of the Boltzmann equation with singular kernel to nonlinear friction equations in the so-called quasi elastic limit. To this aim we introduce a Fourier spectral method for the Boltzmann equation [CITE] and show that the kernel modes that define the spectral method have the correct...
Spline collocation methods for solving second order neutral delay differential equations.
Spline solution of some linear boundary value problems.
Spline-wavelet solution of singularly perturbed boundary problem
Strong convergence estimates for pseudospectral methods
Strong convergence estimates for pseudospectral methods applied to ordinary boundary value problems are derived. The results are also used for a convergence analysis of the Schwarz algorithm (a special domain decomposition technique). Different types of nodes (Chebyshev, Legendre nodes) are examined and compared.