عنوان

Exponentially convergent algorithms for abstract differential equations

303480119X (electronic bk.)

9783034801195 (electronic bk.)

3034801181

9783034801188

b509397

Exponentially convergent algorithms for abstract differential equations

[Book]

Ivan Gavrilyuk, Volodymyr Makarov, Vitalii Vasylyk

[New York] :

Springer,

c2011

1 online resource (viii, 180 p.) :

ill

Frontiers in mathematics

Includes bibliographical references and index

1. Introduction -- 2. Preliminaries -- 3. The first-order equations -- 4. The second-order equations

0

"This book presents new accurate and efficient exponentially convergent methods for abstract differential equations with unbounded operator coefficients in Banach space. These methods are highly relevant for the practical scientific computing since the equations under consideration can be seen as the meta-models of systems of ordinary differential equations (ODE) as well as the partial differential equations (PDEs) describing various applied problems. The framework of functional analysis allows one to obtain very general but at the same time transparent algorithms and mathematical results which then can be applied to mathematical models of the real world. The problem class includes initial value problems (IVP) for first order differential equations with constant and variable unbounded operator coefficients in a Banach space (the heat equation is a simple example), boundary value problems for the second order elliptic differential equation with an operator coefficient (e.g. the Laplace equation), IVPs for the second order strongly damped differential equation as well as exponentially convergent methods to IVPs for the first order nonlinear differential equation with unbounded operator coefficients. For researchers and students of numerical functional analysis, engineering and other sciences this book provides highly efficient algorithms for the numerical solution of differential equations and applied problems"--P. [4] of cover

Exponentially convergent algorithms for abstract differential equations.

9783034801188

SpringerLink

Differential equations

Mathematics

Gavrilyuk, Ivan P

Makarov, Volodymyr

Vasylyk, Vitalii

20120425035347.0

[Book]

Y