Numerical Solution of Partial Differential Equations

This chapter covers the numerical solution of partial differential equations (PDEs), primarily through the use of the finite difference method. Techniques for dealing with elliptic, parabolic and hyperbolic equations are introduced, including iterative methods (such as Gauss–Seidel), explicit and implicit methods, the method of characteristics, and the leapfrog approach (for hyperbolic equations). Two-dimensional viscous flow problems, combined with both heat and mass transfer, are also treated. The use of adaptive grids for immersed objects or curved boundaries is introduced.