Hypersingular Integral Equations of Prandtl’s Type: Theory, Numerical Methods, and Applications

Abstract

In this paper, we propose and justify a spline-collocation method with first-order splines for approximate solution of nonlinear hypersingular integral equations of Prandtl’s type. We obtained the estimates of the convergence rate and the method error. The constructed computational scheme includes a continuous method for solving nonlinear operator equations, which is stable for perturbations of the coefficients and the right-hand sides of equations.

Keywords

• Prandtl equation
• linear and nonlinear singular and hypersingular integral equations
• spline collocation method