Problem solving with well posedness analysis: Part 1

A problem is well posed if: (1) at least one solution exists, (2) at most one solution exists, and (3) the solution is stable. This paper advocates the use of well posedness analysis as a tool to use in problem solving. Well posedness analysis as a problem solving tool has seen too little use, especially in areas such as computer science, discrete mathematics, and software engineering. Here a simple graphics problem initiates illustration of what we mean by the use of well posedness in problem solving. Further, a more challenging problem involving composite grid data distribution is used to show how well posedness analysis can lead to new insights, deeper understanding, and better algorithms in problems of greater complexity.