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. We also list some useful references for those who wish to know
more in related areas.