Research on visualization of the double exponential transformation

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The head investigator arid others have proposed a family of efficent formulas for numerical integration called the double exponential formula. On the other hand, the error of numerical integration can be expressed in terms of a complex integral of a product of the integrand and a function called the characteristic function of the error. In this research we developed a system which computes the characteristic function of the error and gives its contour map on a graphic display. If we.. use this system we can estimate the error of numerical integration by the double exponential formula easily and accurately.The head investigator and opthers had already written several programs which individually compute the characteristic function of the error of sonic particular integral and give its contour map. In the present research we treated the characteristic function in a unified way and developed a system which gives the contour map automatically if the user specifies the parameters such as the type of the integral, the interval of integration, etc. Also in this system we included the*Ooura's formula which compute efficiently Fourier type integrals. Furthermore, we developed a system which ti-eats Newton-Cotes formulas and Gauss type formulas. These programs are written in DIGITAL Visual Fortran, and run on a Windows 95 personal computer system.Finally we developed a system to specify the parameters through several input windows which runs on Microsoft Visual Basic. We wrote a manual to use this system and included it in the report of the present research together with the entire source. code.