Inroduction
The Engineering and Numerical analyses play a very important role in engineering application specially in solving the governing equation of the most important physical phenomena. The principle of engineering analysis is used mainly in solving the ordinary and partial differential equations which is used in the engineering application. On the other hand, in numerical analysis, we focused our attention to solve the linear and the non-linear algebraic equation , the curve fitting, interpolation and the solution of the ordinary and the partial differential equations.
The numerical expression of a scientific statement has traditionally been the manner by which scientists have verified a theoretical description of the physical world. During this century there has been a revolution in both the nature and extent to which this numerical comparison can be made. Indeed, it seems likely that when the history of this century is definitively written, it will be the development of the computer, which will be regarded as its greatest technological achievement - not nuclear power. While it is true that the origins of the digital computer can be traced through the work of Isaac Babbitt, Hermann Hollerith, and others in the nineteenth century, the real advance came after the Second World War when machines were developed that were able to carry out an extended sequence of instructions at a rate that was very much greater than a human could manage. We call such machines programmable.
The electronic digital computer of the sort developed by John von Neumann and others in the 1950s really ushered in the present computer revolution. While it is still to soon to delineate the form and consequences of this revolution, it is already clear that it has forever changed the way in which science and engineering will be done. The entire approach to numerical analysis has changed in the past two decades and that change will most certainly continue rapidly into the future. Prior to the advent of the electronic digital computer, the emphasis in computing was on short cuts and methods of verification which insured that computational errors could be caught before they propagated through the solution. Little attention was paid to "round off error" since the "human computer" could easily control such problems when they were encountered. Now the reliability of electronic machines has nearly eliminated concerns of random error, but round off error can be a persistent problem.