An Introduction to Nonlinear Partial Differential Equations

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The homotopy—perturbation method is employed for solving this class of equations, and the time-fractional derivatives are described in the sense of Caputo. Comparisons are made with those derived by Adomian's decomposition method, revealing that the homotopy perturbation method is more accurate and convenient than the Adomian's decomposition method.

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Furthermore, the results reveal that the approximate solution continuously depends on the time-fractional derivative and the proposed method incorporating the Caputo derivatives is a powerful and efficient technique for solving the fractional differential equations without requiring linearization or restrictive assumptions.

The basis ideas presented in the paper can be further applied to solve other similar fractional partial differential equations. This site uses cookies. By continuing to use this site you agree to our use of cookies.

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Communications in Theoretical Physics. Download Article PDF. An increased focus on hydrogeology and mathematical biology is evident in the new edition. Hints and solutions to selected exercises have been added to the back of the book.

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Nonlinear Partial Differential Equations - 1st Edition

The book emphasizes hyperbolic and parabolic problems and includes a range of applications in the following areas: biology, chemistry, porous media, biological problems, combustion and detonation, traffic flow, water waves, plug flow reactors, and heat transfer. Early chapters offer insight into how to understand problems involving phenomena, how specific equations describe evolutionary processes, and what the terms in such equations describe physically.


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When discussing wave propagination and hyperbolic problems, the text develops algorithms to solve first-order equations and highlights the concept of the weak solution. The material in the book is presented in such a manner that many of the chapters are independent, which allows for instructors' flexibility to design several courses around various topics.


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Toon meer Toon minder. Recensie s This book is an ideal text for applied mathematics courses at the upper-undergraduate and graduate levels. It also serves as a valuable resource for researchers and professionals in the fields of mathematics, biology, engineering, and physics who would like to further their knowledge of PDEs.

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An introduction to nonlinear partial differential equations

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