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### Numerical Solution of Differential Equations: Introduction to Finite Difference and Finite Difference and Finite Element Methods by Zhilin Li, Tao Tang, Zhonghua Qiao

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The purpose of this book is to provide an introduction to finite difference and finite element methods for solving ordinary and partial differential equations of boundary value problems. The book is designed for beginning graduate students, upper level undergraduate students, and students from interdisciplinary areas including engineers and others who need to obtain such numerical solutions. The prerequisite is a basic knowledge of calculus, linear algebra, and ordinary differential equations. Some knowledge of numerical analysis and partial differential equations would also be helpful but not essential.
The emphasis is on the understanding of finite difference and finite element methods and essential details in their implementation with reasonably mathematical theory. Part I considers finite difference methods, and Part II is about finite element methods. In each part, we start with a comprehensive discussion of one-dimensional problems before proceeding to consider two or higher dimensions.
(Zhilin Li)

Book Detail :-
Title: Numerical Solution of Differential Equations
Edition:
Author(s): Zhilin Li
Publisher: Cambridge University Press
Series:
Year: 2018
Pages: 303
Type: PDF
Language: English
ISBN: 9781316678725,1316678725
Country: US

The author Zhilin Li , Center for Research in Scientific Computation, Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA, E-mail: [email protected]

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Book Contents :-
Numerical Solution of Differential Equations written by Zhilin Li cover the following topics. '
PART-I FINITE DIFFERENCE METHODS
3. Finite Difference Methods for 2D Elliptic PDEs
4. FD Methods for Parabolic PDEs
5. Finite Difference Methods for Hyperbolic PDEs
PART-II FINITE ELEMENT METHODS
6. Finite Element Methods for 1D Boundary Value Problems
7. Theoretical Foundations of the Finite Element Method
8. Issues of the FE Method in One Space Dimension
9. The Finite Element Method for 2D Elliptic PDEs
Appendix: Numerical Solutions of Initial Value Problems
Exercises
References
Index

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