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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.

Surla, Katarina, Herceg, Dragoslav, Maličić, Helena (2001)

Novi Sad Journal of Mathematics

Some fourth-order formulae of a certain method of Zurmühl

Grażyna Hobot (1974)

Applicationes Mathematicae

Some nonlinear and nonlocal Sturm-Liouville problems motivated by the problem of flutter.

Belinskiy, B.P., Matthews, J.V. (2009)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Some numerical studies of dynamical systems

E. B. Vul (1989)

Banach Center Publications

Some problems related to discretization of Chaplygin's method

D. Tošić (1983)

Matematički Vesnik

Some properties of solutions to polynomial systems of differential equations.

Carothers, David C., Parker, G.Edgar, Sochacki, James S., Warne, Paul G. (2005)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Some properties of the discontinuous Galerkin method for one-dimensional singularly perturbed problems.

Roos, Hans-Görg, Zarin, Helena (2003)

Novi Sad Journal of Mathematics

Some remarks on an ODE-solver of Kirchgraber.

Sylvia Novo, Jesús Rojo (1992)

Numerische Mathematik

Some remarks on numerical solution of initial problems for systems of differential equations

Tadeusz Jankowski (1979)

Aplikace matematiky

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

A. Olejniczak (1987)

Applicationes Mathematicae

Some results about the pseudospectral approximation of one-dimensional fourth-order problems.

Daniele Funaro, Wilhelm Heinrichs (1990/1991)

Numerische Mathematik

Some uniformly convergent schemes on Shishkin mesh.

Vukoslavčević, Vanja, Rapajić, Sanja, Surla, Katarina (1998)

Novi Sad Journal of Mathematics

Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs

Abdellah Chkifa, Albert Cohen, Ronald DeVore, Christoph Schwab (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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.

Akca, Haydar, Covachev, Valery (2009)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

Special exact curved finite elements

Jitka Křížková (1991)

Applications of Mathematics

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.

Vulanović, Relja (2001)

Novi Sad Journal of Mathematics

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