Numerical methods finite difference calculus

Numerical methods include those based on finite difference calculus. They are ideally suited for tabulated experimental data such as one finds in thermodynamic tables. They also include methods of solving simultaneous linear equations, curve fitting, numerical solution of ordinary and partial differential equations and matrix operations. In this appendix, numerical interpolation, integration, and differentiation are considered. Information about the other topics is available in monographs by Hornbeck [2] and Lanczos [3]. 

The solution of Eq. (2) can also be obtained by a numerical analysis similar to the calculus of finite differences. However, an analytical or semianalytical method based on Eq. (2) is not suitable for discussing the time-dependent distribution function because the calculation is lengthy. 

Several numerical methods for differentiation, integration, and the solution of ordinary and partial differential equations are discussed in Chaps. 4-6 of this book. These methods are based on the concept of finite differences. Therefore, the purpose of this chapter is to develop the systematic terminology used in the calculus of finite differences and to derive the relationships between finite differences and differential operators, which are needed in the numerical solution of ordinary and partial differential equations. 

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