Numerical Integration of Certain Improper Integrals with Complex Integrands.
PENNSYLVANIA STATE UNIV UNIVERSITY PARK APPLIED RESEARCH LAB
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In theoretical fluid mechanics, there is a class of problems associated with calculating the unsteady lift over a row of turbomachine blades that has for its solution a rather complicated function. This function consists of improper integrals whose integrands themselves are complex functions. These integrals cannot be directly evaluated, but previous investigators have successfully integrated them using approximate numerical methods. However, these numerical techniques proved to be inefficient and required substantial amounts of computer time. This report investigates some of the mathematical properties of these integrals and presents a numerical algorithm based upon the Gauss-Legendre method. The Gauss-Legendre scheme proved to be 3.7 times faster than Simpsons rule and the results obtained from the two methods were in good agreement.
- Numerical Mathematics
- Fluid Mechanics