Numerical Time-Dependent Partial Differential Equations for Scientists and Engineers

It is the standard convergence theory that treats all practical ingredients. The book is aimed at numerical analysis and scientific software development. It is strongly influenced by the authors in the area of physical engineering, electrical and optical engineering, applied mathematics, numerical analysis and professional software development. The book covers the first two semesters of the three semester series. Taught at the University of Arizona since 1989. The second semester is based on a semester-long project, finite element method in mechanical engineering, computational physics, biology, chemistry, photonics, etc.

First The three The focus The focus The The The The The, analysis The properties The properties The, sym The properties The; methods of discretization and convergence theory for the initial value problems. The numerical artifacts like diffusion, dithering, dispersion, and anisotropies.

In the second part of the book. The most important part for successful numerical simulation. We adopt a more heuristic and practical approach using numerical methods of investigation and validation. The aim is teach students subtle key issues in order to physics from numerics. The following subjects are addressed: Implementation of transparent and absorbing boundary conditions; Practical stability in the presence of the boundaries and interfaces; Treatment of problems with different temporal / spatial scales or explicit or implicit; preservation of symmetries and additional constraints; physical regularization of singularities; resolution enhancement using adaptive mesh refinement and moving meshes.

• Self contained presentation of key issues in successful numerical simulation


• Accessible to scientists and engineers with diverse background


• Provides analysis of the dispersion rela on, symmetries, particular solutions and instabilities of the partial differential equations

Preface;
Chapter 1 - Overview of Properties Partial Differential equations;
Chapter 2 - Methods of Discretization;
Chapter 3 - Convergence Theory for Initial Value Problems;
Chapter 4 - Numerical Boundary Conditions;
Chapter 5 - Problems with Multiple Temporal and Spatial Scales;
Chapter 6 - Nonuniform, Adaptive and Moving Grids;