ABSTRACT
In the previous chapter linear iterative methods were used to approximate the solution to two dimensional steady state space problems. This often results in three nested loops where the outermost loop is the iteration of the method and the two innermost loops are for the two space directions. If the two dimensional problem is nonlinear or if the problem is linear and in three directions, then there must be one additional loop. In the first three sections, nonlinear problems, the Picard and Newton methods are introduced. The last three sections are devoted to three space dimension problems, and these often require the use of high performance computing. Applications will include linear and nonlinear heat transfer, and in the next chapter space dependent population models, image restoration and value of option contracts. A basic introduction to nonlinear methods can be found in Burden and Faires [4]. A more current description of nonlinear methods can be found in C. T. Kelley [11].
