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Approximate Analytical Methods for Solving Ordinary Differential Equations (Paperback)
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Approximate Analytical Methods for Solving Ordinary Differential Equations (Paperback)
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Approximate Analytical Methods for Solving Ordinary Differential
Equations (ODEs) is the first book to present all of the available
approximate methods for solving ODEs, eliminating the need to wade
through multiple books and articles. It covers both
well-established techniques and recently developed procedures,
including the classical series solution method, diverse
perturbation methods, pioneering asymptotic methods, and the latest
homotopy methods. The book is suitable not only for mathematicians
and engineers but also for biologists, physicists, and economists.
It gives a complete description of the methods without going deep
into rigorous mathematical aspects. Detailed examples illustrate
the application of the methods to solve real-world problems. The
authors introduce the classical power series method for solving
differential equations before moving on to asymptotic methods. They
next show how perturbation methods are used to understand physical
phenomena whose mathematical formulation involves a perturbation
parameter and explain how the multiple-scale technique solves
problems whose solution cannot be completely described on a single
timescale. They then describe the Wentzel, Kramers, and Brillown
(WKB) method that helps solve both problems that oscillate rapidly
and problems that have a sudden change in the behavior of the
solution function at a point in the interval. The book concludes
with recent nonperturbation methods that provide solutions to a
much wider class of problems and recent analytical methods based on
the concept of homotopy of topology.
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