On convergence of the polynomial collocation method for singular integral equations and periodic pseudodifferential equations (Q5925786)

The polynomial collocation method for singular integral equations, periodic pseudodifferential equations and systems of pseudodifferential equations in Sobolev spaces is presented. The results show that the polynomial collocation method converges for a wider class of equations than the spline collocation method. Moreover, the calculation schemes of polynomial collocation methods are easier than those of spline collocation methods for a wide range of equations including singular integral and integro-differential equations.