FINITE DIFFERENCE SCHEMES AND PARTIAL DIFFERENTIAL EQUATIONS

This book provides a unified and accessible introduction to the basic theory of finite difference schemes applied to the numerical solution of partial differential equations. Originally published in 1989, its objective remains to present the basic methods necessary to perform finite difference schemes and to understand the theory underlying the schemes. This second edition is one of the few texts that not only presents the theory of stability in a rigorous and clear manner but also discusses the theory of initial-boundary value problems in relation to finite difference schemes. The material on elliptic partial differential equations found in later chapters provides an introduction to more advanced texts. This updated edition includes several important modifications. The notion of a stability domain is now included in the definition of stability and is generally more prevalent throughout. Many new figures and tables clarify important concepts and illustrate the properties of finite difference schemes.