Solving nonlinear boundary value problems using He's polynomials and Padé approximants.
Solving ordinary differential equation systems by approximation in a graphical way.
Solving the systems of equations arising in the discretization of some nonlinear p.d.e.'s by implicit Runge-Kutta methods
Some applications of the Pascal matrix to the study of numerical methods for differential equations
In this paper we introduce and analyze some relations between the Pascal matrix and a new class of numerical methods for differential equations obtained generalizing the Adams methods. In particular, we shall prove that these methods are suitable for solving stiff problems since their absolute stability regions contain the negative half complex plane.
Some comparisons of difference schemes on meshes of Shishkin and Bakhvalov type.
Some fourth-order formulae of a certain method of Zurmühl
Some nonlinear and nonlocal Sturm-Liouville problems motivated by the problem of flutter.
Some numerical studies of dynamical systems
Some problems related to discretization of Chaplygin's method
Some properties of solutions to polynomial systems of differential equations.
Some properties of the discontinuous Galerkin method for one-dimensional singularly perturbed problems.
Some remarks on an ODE-solver of Kirchgraber.
Some remarks on numerical solution of initial problems for systems of differential equations
This paper presents a class of numerical methods for approximate solution of systems of ordinary differential equations. It is shown that under certain general conditions these methods are convergent for sufficiently small step size. We give estimations of errors which are better than the known ones.
Some remarks on the intervals of stability of Runge-Kutta methods after Richardson extrapolation
Some results about the pseudospectral approximation of one-dimensional fourth-order problems.
Some uniformly convergent schemes on Shishkin mesh.
Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs
The numerical approximation of parametric partial differential equations is a computational challenge, in particular when the number of involved parameter is large. This paper considers a model class of second order, linear, parametric, elliptic PDEs on a bounded domain D with diffusion coefficients depending on the parameters in an affine manner. For such models, it was shown in [9, 10] that under very weak assumptions on the diffusion coefficients, the entire family of solutions to such equations...
Spatial discretization of an impulsive Cohen-Grossberg neural network with time-varying and distributed delays and reaction-diffusion terms.
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.
Special meshes and higher-order schemes for singularly perturbed boundary value problems.