Chebyshev spectral method for one class of singular integro-differential equations

Approximate numerical algorithms for solving singular integro-differential equations of the generalized Prandtl equation type have been developed. In the proposed approximate schemes, the solution of the equation is expanded in terms of an orthogonal basis of Chebyshev polynomials. By using well-known spectral relations, an analytical expression is obtained for the singular component of the equation. As a consequence, the proposed method has excellent accuracy and the approximate solution converges exponentially with respect to the degree of the interpolation polynomials. The computational capabilities of the method are demonstrated using a test example.