Numerical methods for nonlinear partial differential equations

By:

Bartels, Soren

Series: Springer Series in Computational Mathematics ; Vol. 47Publication details: Cham, Switzerland: Springer, 2015.Description: x, 393 p. hbk.: 24 cmISBN:

9783319137964

Subject(s):

DDC classification:

515.353 BAR

Summary: The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations. https://link.springer.com/book/10.1007/978-3-319-13797-1#overview

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Item type	Current library	Collection	Call number	Copy number	Status	Barcode
Books	IIT Gandhinagar	General	515.353 BAR (Browse shelf(Opens below))	1	Available	035391

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Previous	515.35221 GOC Numerical methods for bifurcations of dynamical equilibria	515.353 CAR Nonsmooth variational problems and their inequalities : comparison principles and applications	515.353 AMB Optimal transportation and applications: lectures given at the C.I.M.E. summer school held in Martina Franca, Italy, September 2–8, 2001	515.353 BAR Numerical methods for nonlinear partial differential equations	515.353 BEN Asymptotic analysis for periodic structures	515.353 CAF Nonlinear partial differential equations	515.353 CAN One-dimensional heat equation, Vol. 23	Next

Includes Bibliographical References and Index

The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.

https://link.springer.com/book/10.1007/978-3-319-13797-1#overview

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