Numerical Solutions to Partial Differential Equations with Finite Difference Methods

This book covers finite difference methods for two-point boundary value problems, elliptic equations, parabolic equations, hyperbolic equations, high-dimensional evolution equations, fractional differential equations, Schrodinger equations, the Burgers’ equation and the Korteweg-de Vries equation.

The book strives to achieve:

(a) Featured content. The finite difference method is introduced emphatically.

(b) Scattered difficulty. For the finite difference method, authors start from the two-point boundary value problem of ordinary differential equation and introduce the concepts of finite difference method and frequently used analysis techniques, and then apply these concepts and techniques to solve other partial differential equations.

(c) Emphasis on practicability of the finite difference methods. First authors use examples to demonstrate theoretical results, and then ask students to imitate, and finally master the numerical methods.

The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.