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Springer Series in Computational Mathematics

Springer Series in Computational Mathematics
61 Volumes | 1983 - 2021


This is basically a numerical analysis series in which high-level monographs are published. We develop this series aiming at having more publications in it which are closer to applications. There are several volumes in the series which are linked to some mathematical software. This is a list of all titles published in this series:

All books of the series Springer Series in Computational Mathematics

2021 | Book


Algebraic Analysis of Numerical Methods

B-series, also known as Butcher series, are an algebraic tool for analysing solutions to ordinary differential equations, including approximate solutions. Through the formulation and manipulation of these series, properties of numerical methods …

2020 | Book

Krylov Methods for Nonsymmetric Linear Systems

From Theory to Computations

This book aims to give an encyclopedic overview of the state-of-the-art of Krylov subspace iterative methods for solving nonsymmetric systems of algebraic linear equations and to study their mathematical properties. Solving systems of algebraic …

2019 | Book

Numerical Methods for Fractional Differentiation

This book discusses numerical methods for solving partial differential and integral equations, as well as ordinary differential and integral equations, involving fractional differential and integral operators. Differential and integral operators …

2019 | Book

Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations

Recently, various mathematical problems have been solved by computer-assisted proofs, among them the Kepler conjecture, the existence of chaos, the existence of the Lorenz attractor, the famous four-color problem, and more. In many cases …

2019 | Book

Tensor Spaces and Numerical Tensor Calculus

Special numerical techniques are already needed to deal with n × n matrices for large n. Tensor data are of size n × n ×...× n=nd, where nd exceeds the computer memory by far. They appear for problems of high spatial dimensions. Since standard …

2018 | Book

Advanced Boundary Element Methods

Treatment of Boundary Value, Transmission and Contact Problems

This book is devoted to the mathematical analysis of the numerical solution of boundary integral equations treating boundary value, transmission and contact problems arising in elasticity, acoustic and electromagnetic scattering. It serves as the …

2017 | Book

Elliptic Differential Equations

Theory and Numerical Treatment

This book simultaneously presents the theory and the numerical treatment of elliptic boundary value problems, since an understanding of the theory is necessary for the numerical analysis of the discretisation. It first discusses the Laplace …

2016 | Book

Retarded Potentials and Time Domain Boundary Integral Equations

A Road Map

This book offers a thorough and self-contained exposition of the mathematics of time-domain boundary integral equations associated to the wave equation, including applications to scattering of acoustic and elastic waves. The book offers two …

2016 | Book

Finite Element Methods for Incompressible Flow Problems

This book explores finite element methods for incompressible flow problems: Stokes equations, stationary Navier-Stokes equations and time-dependent Navier-Stokes equations. It focuses on numerical analysis, but also discusses the practical use of …

2015 | Book

Numerical Methods for Nonlinear Partial Differential Equations

The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods

2015 | Book

Discontinuous Galerkin Method

Analysis and Applications to Compressible Flow

The subject of the book is the mathematical theory of the discontinuous Galerkin method (DGM), which is a relatively new technique for the numerical solution of partial differential equations. The book is concerned with the DGM developed for ellip

2015 | Book

Hierarchical Matrices: Algorithms and Analysis

This self-contained monograph presents matrix algorithms and their analysis. The new technique enables not only the solution of linear systems but also the approximation of matrix functions, e.g., the matrix exponential. Other applications include

2014 | Book

Analysis of Finite Difference Schemes

For Linear Partial Differential Equations with Generalized Solutions

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

Finite difference methods are a classical c

2014 | Book

The Concept of Stability in Numerical Mathematics

In this book, the author compares the meaning of stability in different subfields of numerical mathematics.

Concept of Stability in numerical mathematics opens by examining the stability of finite algorithms. A more precise definition of sta

2013 | Book

Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials

The purpose of this book is to provide an up-to-date introduction to the time-domain finite element methods for Maxwell’s equations involving metamaterials. Since the first successful construction of a metamaterial with both negative permittivity and

2013 | Book

Mixed Finite Element Methods and Applications

Non-standard finite element methods, in particular mixed methods, are central to many applications. In this text the authors, Boffi, Brezzi and Fortin present a general framework, starting with a finite dimensional presentation, then moving on to

2012 | Book

Tensor Spaces and Numerical Tensor Calculus

Special numerical techniques are already needed to deal with nxn matrices for large n.Tensor data are of size nxnx...xn=n^d, where n^d exceeds the computer memory by far. They appear for problems of high spatial dimensions. Since standard methods fai

2011 | Book

Boundary Element Methods

This work presents a thorough treatment of boundary element methods (BEM) for solving strongly elliptic boundary integral equations obtained from boundary reduction of elliptic boundary value problems in $\mathbb{R}^3$. The book is self-contained, t

2011 | Book

Spectral Methods

Algorithms, Analysis and Applications

Along with finite differences and finite elements, spectral methods are one of the three main methodologies for solving partial differential equations on computers. This book provides a detailed presentation of basic spectral algorithms, as well a

2011 | Book

Numerical Methods for Two-phase Incompressible Flows

This book is the first monograph providing an introduction to and an overview of numerical methods for the simulation of two-phase incompressible flows. The Navier-Stokes equations describing the fluid dynamics are examined in combination with mod