Fundamental Concepts in the Numerical Solution of Differential Equations



This book is relatively short, about 200 pages, organized into seven chapters. The first chapter sets the scope and objectives and contains a note on notation. The next chapter contains the fundamental concepts that are the key to the presentation and the authors' philosophy on numerical methods. Chapters 4–6 treat elliptic (Poisson's equation), parabolic (the diffusion equation), and hyperbolic partial differential equations, respectively. The last chapter shows the solutions of certain cases with singularities and nonlinear behavior. The boundary element method is briefly discussed in chapter 4; the method of characteristics is discussed in chapter 6.