Double exponential integration method and its application to oscillatory integrals

Numerical calculation of highly oscillatory integrals has been subject of the many investigations in science. There are many numerical methods to calculate the highly oscillatory integrals which has kernel e^(i?g(x)). Double exponential oscillatory method is one of the methods. In this thesis, optimality of the Double exponential oscillatory integrating formula is investigated and numerical examples are given whichs shows the applicability of this method. Furthermore, we compare the result of our method with other method which was used previously and the results are documented on graphs and tables.