Spline collocation methods for partial differential equations : with applications in R / William E. Schiesser.

Format:

Book

Author/Creator:

Schiesser, W. E., author.

Language:

English

Subjects (All):

Differential equations, Partial--Mathematical models.

Differential equations, Partial.

Spline theory.

Mathematical models.

Physical Description:

xv, 549 pages ; 25 cm

Place of Publication:

Hoboken, NJ : John Wiley & Sons, Inc., 2017.

Summary:

A comprehensive approach to numerical partial differential equations, Spline Collocation Methods for Partial Differential Equations combines the collocation analysis of partial differential equations (PDEs) with the method of lines (MOL) in order to simplify the solution process. Using a series of example applications, the author delineates the main features of the approach in detail, including an established mathematical framework. The book also clearly demonstrates that spline collocation can offer a comprehensive method for numerical integration of PDEs when it is used with the MOL in which spatial (boundary value) derivatives are approximated with splines, including the boundary conditions. R, an open-source scientific programming system, is used throughout for programming the PDES and numerical algorithms, and each section of code is clearly explained. As a result, readers gain a complete picture of the model and its computer implementation without having to fill in the details of the numerical analysis, algorithms, or programming. The presentation is not heavily mathematical, and in place of theorems and proofs, detailed example applications are provided. Appropriate for scientists, engineers, and applied mathematicians, Spline Collocation Methods for Partial Differential Equations: Introduces numerical methods by first presenting basic examples followed by more complicated applications, Employs R to illustrate accurate and efficient solutions of the PDE models, Presents spline collocation as a comprehensive approach to the numerical integration of PDEs and an effective alternative to other, well established methods, Discusses how to reproduce and extend the presented numerical solutions, Identifies the use of selected algorithms, such as the solution of nonlinear equations and banded or sparse matrix processing, Features a companion website that provides the related R routines, Spline Collocation Methods for Partial Differential Equations is a valuable reference and/or self-study guide for academics, researchers, and practitioners in applied mathematics and engineering, as well as for advanced undergraduates and graduate-level students. Book jacket.

Contents:

One-dimensional PDEs

Multidimensional PDEs

Navier-Stokes, Burgers equations

Korteweg-deVries equation

Maxwell equations

Poisson-Nernst-Planck equations

Fokker-Planck equation

Fisher-Kolmogorov equation

Klein-Gordon equation

Boussinesq equation

Cahn-Hilliard equation

Camassa-Holm equation

Burgers-Huxley equation

Gierer-Meinhardt equations

Keller-Segel equations

Fitzhugh-Nagumo equations

Euler-Poisson-Darboux equation

Kuramoto-Sivashinsky equation

Einstein-Maxwell equations.

Notes:

Includes bibliographical references and index.

Other Format:

Online version: Schiesser, W.E. Spline collocation methods for partial differential equations.

ISBN:

9781119301035

1119301033

OCLC:

963914982

Publisher Number:

99974740212