Numerical Example

Owing to the developments and applications of computer science, ma­ thematicians began to take a serious interest in the applications of number theory to numerical analysis about twenty years ago. The progress achieved has been both important practically as well as satisfactory from the theoretical view point.

Using Excel to make Numerical Predictions on Time Series data

This book familiarizes readers with the practical application of the numerical simulation technique to solve complex analytical problems in different industries and sciences.

Computational Hydraulics introduces the concept of modeling and the contribution of numerical methods and numerical analysis to modeling. it provides a concise and comprehensive description of the basic hydraulic principles, and the problems addressed by these principles in the aquatic environment. Flow equations, analytical and numerical solutions are included.

The second edition of this book fully preserves the character of the first edition to combine the detailed physical modeling of mechatronic systems and their precise numerical simulation using the Finite Element (FE) method. Most of the text and general appearance of the previous edition were retained, while the coverage was extended and the presentation improved.

Numerical Python by Robert Johansson shows you how to leverage the numerical and mathematical capabilities in Python, its standard library, and the extensive ecosystem of computationally oriented Python libraries, including popular packages such as NumPy, SciPy, SymPy, Matplotlib, Pandas, and more, and how to apply these software tools in computational problem solving.

Reaction-diffusion equations are typical mathematical models in biology, chemistry and physics. These equations often depend on various parame­ ters, e. g. temperature, catalyst and diffusion rate, etc. Moreover, they form normally a nonlinear dissipative system, coupled by reaction among differ­ ent substances. The number and stability of solutions of a reaction-diffusion system may change abruptly with variation of the control parameters. Cor­ respondingly we see formation of patterns in the system, for example, an onset of convection and waves in the chemical reactions. This kind of phe­ nomena is called bifurcation. Nonlinearity in the system makes bifurcation take place constantly in reaction-diffusion processes. Bifurcation in turn in­ duces uncertainty in outcome of reactions. Thus analyzing bifurcations is essential for understanding mechanism of pattern formation and nonlinear dynamics of a reaction-diffusion process. However, an analytical bifurcation analysis is possible only for exceptional cases. This book is devoted to nu­ merical analysis of bifurcation problems in reaction-diffusion equations. The aim is to pursue a systematic investigation of generic bifurcations and mode interactions of a dass of reaction-diffusion equations. This is realized with a combination of three mathematical approaches: numerical methods for con­ tinuation of solution curves and for detection and computation of bifurcation points; effective low dimensional modeling of bifurcation scenario and long time dynamics of reaction-diffusion equations; analysis of bifurcation sce­ nario, mode-interactions and impact of boundary conditions.

Mathematical modeling is an active area of applied mathematics. At its beginning, engineers were the main practitioners of this area of mathematics, developing mathematical models to solve engineering problems in natural sciences.

A Foundation Course to become an expert in Engineering Mechanics-with Regular Updates

The Essentials of Root Finding and Numerical Integration in MATLAB