Nonlinear Partial Differential Equations in Engineering: Mathematics in Science and Engineering: A Series of Monographs and Textbooks, Vol. 18 - Softcover

Ames, W. F.

Softcover

ISBN 10: 1483209490 ISBN 13: 9781483209494

Publisher: Academic Press, 2016

Synopsis

Nonlinear Partial Differential Equations in Engineering discusses methods of solution for nonlinear partial differential equations, particularly by using a unified treatment of analytic and numerical procedures. The book also explains analytic methods, approximation methods (such as asymptotic processes, perturbation procedures, weighted residual methods), and specific numerical procedures associated with these equations. The text presents exact methods of solution including the quasi-linear theory, the Poisson-Euler-Darboux equation, a general solution for anisentropic flow, and other solutions obtained from ad hoc assumptions. The book explores analytic methods such as an ad hoc solution from magneto-gas dynamics. Noh and Protter have found the Lagrange formulation to be a convenient vehicle for obtaining "soft" solutions of the equations of gas dynamics. The book notes that developing solutions in two and three dimensions can be achieved by employing Lagrangian coordinates. The book explores approximate methods that use analytical procedures to obtain solutions in the form of functions approximating solutions of nonlinear problems. Approximate methods include integral equations, boundary theory, maximum operation, and equations of elliptic types. The book can serve and benefit mathematicians, students of, and professors of calculus, statistics, or advanced mathematics.

Edition details

• Publisher: Academic Press
• Publication date: 2016
• ISBN 10: 1483209490
• ISBN 13: 9781483209494
• Binding: Paperback
• Language: English
• Number of pages: 526