This review paper is devoted to the numerical analysis of abstract differential equations in
Banach spaces. Most of the finite-difference, finite-element, and projection methods can be …

This book develops a systematic and rigorous mathematical theory of finite difference
methods for linear elliptic, parabolic and hyperbolic partial differential equations with …

Computational Hydraulics introduces the concept of modeling and the contribution of
numerical methods and numerical analysis to modeling. It provides a concise and …

We consider a Dirichlet boundary-value problem for the three-dimensional convection-
diffusion equations with constant coefficients in the unit cube. A high order compact finite …

We investigate the convergence of difference schemes for the one-dimensional heat
equation when the coefficient at the time derivative (heat capacity) is c\left(x\right)=1+Kδ\left …

The paper deals with such estimates of the rate of convergence of difference methods, which
are compatible with the smoothness of the exact solution u∈ W 2 m (Ω), m> 0.5, of elliptic …

We study the convergence of the finite-difference schemes for the first initial-boundary value
problem for linear second-order parabolic equations with variable coefficients. Using the …

We consider an initial boundary‐value problem for the generalized Benjamin–Bona–
Mahony equation. A three‐level conservative difference schemes are studied. The obtained …

We investigate the convergence of difference schemes for the one-dimensional heat
equation with variable (time-dependent) operator and the coefficient at the time derivative …

In this paper we study the convergence of a finite difference scheme that approximates the
third boundary-value problem for an elliptic equation with variable coefficients on a unit …