Geodesic
Two methods for direct numerical integration of the Prandtl equation and comparative analysis between them
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 8, pp. 1281-1288 Cet article a éte moissonné depuis la source Math-Net.Ru

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Two methods based on quadrature formulas are proposed for the direct numerical integration of Prandtl’s singular integro-differential equation. In the first method, Prandtl’s equation is solved directly by applying the method of mechanical quadrature and the circulation along an airfoil section is determined. In the second method, Prandtl’s equation is rewritten for the circulation derivative, which is determined by applying mechanical quadratures, and the circulation is then reconstructed using the same quadrature formulas. Both methods are analyzed numerically and are shown to converge. Their convergence rates are nearly identical, while the second method requires much more CPU time than the first one. 
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A. V. Sahakyan; N. N. Shavlakadze. Two methods for direct numerical integration of the Prandtl equation and comparative analysis between them. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 8, pp. 1281-1288. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_8_a4/

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