ABSTRACT

To this purpose we define a discrete metric space M^ and a discrete metric pN and obtain the following result.

Theorem 2 The space (M#, px) is a complete metric space and there exists a unique non-trivial solution of (8) in M#. In addition the sequence of iterations yr^x — S^yrN, starting with any grid function in M^ converges to the solution. Furthermore, it can be shown that this method, consisting of iteration in MN, i.e. letting r —> oo, and refining the grid IN, i.e. letting N —» oo, is convergent.