Ostrowski Type Inequalities and Applications in Numerical Integration

Mechanics the oldest branch of physics to this day remains the basis for modern technology. This is especially evident with regard to the oil and gas industry. Almost all of the technological processes in these branches of industry from the drilling of wells to the transporting of oil and gas products via pipelines are mechanical in their nature. The processes of the development of oil and gas deposits are of primary importance in the whole technological chain of oil and gas extraction from the rocks and their transportation to the customer. The use of scientific methods for improving technology is a long-established tradition of oil and gas industry. For the Western reader it is enough to mention the fundamental treatises by the outstanding American research scientist and engineer M. Muskat (1937 1949) as well as the excellent books of Scheidegger (1960) and Collins (1961) which combine practical goals with profound theoretical analysis. The initiators of the application of mechanics for solving problems of the oil and gas industry in the U.S.S.R. were V.G. Shukhov (1981) and LS. Leibenzon (1934 1947 1953 1955) whose works constitute admirable examples of Soviet technical thought. During recent times the magnitude of oil and gas extraction has increased immensely and many reservoirs with complicated physical and geological properties have therefore entered into the development. The fundamental problem of enhancing oil and gas recovery from rocks has been intensively and deeply analyzed.