Numerical integration of space fractional partial differential equations. Vol. 2: Applications from classical integer PDEs.

*(English)*Zbl 1384.65064
Synthesis Lectures on Mathematics and Statistics 20. San Rafael, CA: Morgan & Claypool Publishers (ISBN 978-1-68173-209-1/pbk; 978-1-68173-210-7/ebook). xii, 183-375 (2018).

This book is organized as follows. The book is divided into 3 chapters and it is the continuation from Volume I, see [Numerical integration of space fractional partial differential equations. Vol. 1: Introduction to algorithms and computer coding in R. San Rafael, CA: Morgan & Claypool Publishers (2018; Zbl 1384.65063)].

Preface.

Chapter 6: Simultaneous SFPDEs. Chapter 6 consists of Introduction: Simultaneous SFPDEs: Main program; ODE/MOL routine; SFPDEs output; Variation of the parameters; Summary and conclusions.

Chapter 7: Two-sided SFPDEs. Chapter 7 consists of: Introduction; Two-sided convective SFPDE, Caputo derivatives; Main program; ODE/MOL routine; SFPDE output; Main program; ODE/MOL routine; SFPDE output; Summary and conclusions.

Chapter 8: Integer to fractional extensions. Chapter 8 consists of: Introduction; Fractional diffusion equation; Main program, Dirchlet boundary condition (BCs); ODE/MOL routine; Model output; Main program, Neumann BCs; ODE/MOL routine; Model output.

In addition it contains: Authors’ Biographies and Index.

The book is well organized and presents the most important applications from space fractional partial differential equations. Suitable for senior under graduate and graduate students as well as practical engineers and researchers interested in numerical integration of space fractional partial differential equations.

Preface.

Chapter 6: Simultaneous SFPDEs. Chapter 6 consists of Introduction: Simultaneous SFPDEs: Main program; ODE/MOL routine; SFPDEs output; Variation of the parameters; Summary and conclusions.

Chapter 7: Two-sided SFPDEs. Chapter 7 consists of: Introduction; Two-sided convective SFPDE, Caputo derivatives; Main program; ODE/MOL routine; SFPDE output; Main program; ODE/MOL routine; SFPDE output; Summary and conclusions.

Chapter 8: Integer to fractional extensions. Chapter 8 consists of: Introduction; Fractional diffusion equation; Main program, Dirchlet boundary condition (BCs); ODE/MOL routine; Model output; Main program, Neumann BCs; ODE/MOL routine; Model output.

In addition it contains: Authors’ Biographies and Index.

The book is well organized and presents the most important applications from space fractional partial differential equations. Suitable for senior under graduate and graduate students as well as practical engineers and researchers interested in numerical integration of space fractional partial differential equations.

Reviewer: Seenith Sivasundaram (Daytona Beach)

##### MSC:

65M20 | Method of lines for initial value and initial-boundary value problems involving PDEs |

35R11 | Fractional partial differential equations |

65-02 | Research exposition (monographs, survey articles) pertaining to numerical analysis |

65Y15 | Packaged methods for numerical algorithms |