Solving Nonlinear Partial Differential Equations with Maple and Mathematica

by Inna K. Shingareva, Carlos Lizárraga-Celaya

The emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple and Mathematica, facilitates a deeper understanding of the subject. Among a big number of CAS, we choose the two systems, Maple and Mathematica, that are used worldwide by students, research mathematicians, scientists, and engineers. As in the our previous books, we propose the idea to use in parallel both systems, Maple and Mathematica, since in many research problems frequently it is required to compare independent results obtained by using different computer algebra systems, Maple and/or Mathematica, at all stages of the solution process. One of the main points (related to CAS) is based on the implementation of a whole solution method (e.g. starting from an analytical derivation of exact governing equations, constructing discretizations and analytical formulas of a numerical method, performing numerical procedure, obtaining various visualizations, and comparing the numerical solution obtained with other types of solutions considered in the book, e.g. with asymptotic solution).

370 pages, Paperback

First published January 1, 2011

About the author

Inna K. Shingareva was born and grew up in Moscow, studied (in parallel) music
(piano, Special Music School, Moscow State Tchaikovsky Conservatory) and mathematics (Moscow Institute of Electronics and Mathematics). She received a Ph.D. in Physics and Mathematics (1995, Institute for Problems in Mechanics of the Russian Academy of Sciences). Since 2000 she is a scientist and professor in the Mathematics Department at the University of Sonora (México). Her main research areas are in Mathematical Equations, Fluid Mechanics, Mathematical Physics, Computer Algebra, Scientific Publishing, Science Education, Mathematics and Music.