Spherical and plane integral operators for PDEs : construction, analysis, and applications / Karl K. Sabelfeld, Irina A. Shalimova.

Format:

Book

Author/Creator:

Sabelʹfelʹd, K. K. (Karl Karlovich)

Contributor:

Shalimova, I. A.

Language:

English

Subjects (All):

Differential equations, Partial.

Integral operators.

Physical Description:

1 online resource (338 p.)

Edition:

1st ed.

Place of Publication:

Berlin ; Boston : Walter de Gruyter GmbH & Company, [2013]

Language Note:

English

Summary:

The book presents integral formulations for partial differential equations, with the focus on spherical and plane integral operators. The integral relations are obtained for different elliptic and parabolic equations, and both direct and inverse mean value relations are studied. The derived integral equations are used to construct new numerical methods for solving relevant boundary value problems, both deterministic and stochastic based on probabilistic interpretation of the spherical and plane integral operators.

Contents:

Front matter

Preface

Contents

1. Introduction

2. Scalar second-order PDEs

3. High-order elliptic equations

4. Triangular systems of elliptic equations

5. Systems of elasticity theory

6. The generalized Poisson formula for the Lamé equation

7. Spherical means for the stress and strain tensors

8. Random Walk on Spheres method

9. Random Walk on Fixed Spheres for Laplace and Lamé equations

10. A stochastic spectral projection method for solving PDEs for some classes of domains

11. Stochastic boundary collocation and spectral methods

12. Solution of 2D elasticity problems with random loads

13. Boundary value problems for some elliptic PDEs with random boundary conditions

Bibliography

Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (ebrary, viewed December 24, 2013).

ISBN:

9783110315332

3110315335

OCLC:

862612009