The use of modified quasi-interpolatory splines for the solution of the Prandtl equation

Modified quasi-interpolatory splines are used for the numerical solution of the generalized Prandtl equation. A Nystrِm type method is applied, based on inserting in the integral equation a modified quasi-interpolatory spline instead of the unknown function. The integral equation can then be solved by collocation and evaluation of suitable Cauchy principal value integrals. Necessary conditions have been established for demonstrating that the approximate solution of the equation converges to the true solution.