Parabolic partial differential equations (PDEs) are fundamental in modelling a wide range of diffusion processes in physics, finance and engineering. The numerical approximation of these equations ...

Our approach to backward error analysis is based on a simple recursive definition of the modified vector fields that does not require explicit Taylor series expansion of the numerical method and the ...

Numerical Solution of Systems of Linear Equations, Iterative Methods Formulation and analysis of basic stationary methods e.g. Gauss-Jacobi, Gauss-Seidel. The numerical solution of Poisson's equation.

This paper provides an error analysis for the Crank-Nicolson method of time discretization applied to spatially discrete Galerkin approximations of the nonstationary Navier-Stokes equations.