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- Georgios Akrivis
- IEEE Computational Science and Engineering
- 1998

fix differential equations, both ordinary and partial. It consists of three parts. Part I contains six chapters and is devoted to initial-value problems for ODEs. Parts I1 and I11 deal with PDEs,â€¦ (More)

- Georgios Akrivis, Michel Crouzeix, Charalambos Makridakis
- Math. Comput.
- 1998

We approximate the solution of initial boundary value problems for nonlinear parabolic equations. In space we discretize by finite element methods. The discretization in time is based on linearâ€¦ (More)

- Georgios Akrivis, Michel Crouzeix, Charalambos Makridakis
- Numerische Mathematik
- 1999

Efficient combinations of implicit and explicit multistep methods for nonlinear parabolic equations were recently studied in [1]. In this note we present a refined analysis to allow more generalâ€¦ (More)

- Georgios Akrivis, Charalambos Makridakis, Ricardo H. Nochetto
- Math. Comput.
- 2006

Abstract. We derive optimal order a posteriori error estimates for time discretizations by both the Crankâ€“Nicolson and the Crankâ€“Nicolsonâ€“Galerkin methods for linear and nonlinear parabolicâ€¦ (More)

- Georgios Akrivis, Michel Crouzeix
- Math. Comput.
- 2004

We construct and analyze combinations of rational implicit and explicit multistep methods for nonlinear parabolic equations. The resulting schemes are linearly implicit and include as particularâ€¦ (More)

- Georgios Akrivis
- 2014

We analyze the discretization of an initial-boundary value problem for the cubic SchrÃ¶dinger equation in one space dimension by a Crankâ€“Nicolsonâ€“type finite difference scheme. We then linearize theâ€¦ (More)

- Georgios Akrivis, V. A. Dougalis, Ohannes A. Karakashian, W. R. McKinney
- SIAM J. Scientific Computing
- 2003

We consider the initial-value problem for the radially symmetric nonlinear SchrÃ¶dinger equation with cubic nonlinearity (NLS) in d = 2 and 3 space dimensions. To approximate smooth solutions of thisâ€¦ (More)

- Georgios Akrivis, Charalambos Makridakis, Ricardo H. Nochetto
- Numerische Mathematik
- 2011

We unify the formulation and analysis of Galerkin and Rungeâ€“Kutta methods for the time discretization of parabolic equations. This, together with the concept of reconstruction of the approximateâ€¦ (More)

We approximate the solutions of an initialand boundary-value problem for nonlinear SchrÃ¶dinger equations (with emphasis on the â€˜cubicâ€™ nonlinearity) by two fully discrete finite element schemes basedâ€¦ (More)

- Georgios Akrivis, Christian Lubich
- Numerische Mathematik
- 2015

Quasi-linear parabolic equations are discretised in time by fully implicit backward difference formulae (BDF) as well as by implicitâ€“explicit and linearly implicit BDF methods up to order 5. Underâ€¦ (More)