**9**, 1, pp. 5-18, 1961

### Numeryczne Modelowanie Procesów Fizycznych

So far, the modern computer seems to have caused less change in this situation than these considerations would lead one to expect. In particular, the numerical methods for solving problems have changed little from the special function days. Thus, there arise the following basic questions:

a) Are the methods designed for small numbers of arithmetic operations and maximum utilization of tabulated results suitable for the computers?

b) What criteria can be used for the development of numerical methods under the new conditions? These ideas are discussed in detail and certain aspects of the use of exponential functions as the base for asymptotic integration methods are discussed in the light of applications to problems of diffusion and beam theory. The selected approach stresses the numerical simulation aspect in order to demonstrate how physical insight and knowledge of the mathematical features of the sought solutions can be combined for the purpose of the design of numerical methods.

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