ABSTRACT
Many problems of science and engineering are reduced to quantifiable form through the process of mathematical modelling. The equations arising often are expressed in terms of the unknown quantities and their derivatives. Such equations are called differential equations. The solution of these equations has exercised the ingenuity of great mathematicians since the time of Newton, and many powerful analytical techniques are available to the modern scientist. However, prior to the development of sophisticated computing machinery, only a small fraction of the differential equations of applied mathematics were accurately solved. Although a model equation based on established physical laws may be constructed, analytical tools frequently are inadequate for its solution. Such a restriction makes impossible any long-term predictions which might be sought. In order to achieve any solution it was necessary to simplify the differential equation, thus compromising the validity of the mathematical modelling which had been applied.
