Supergeometric Convergence of Spectral Collocation Methods for Weakly Singular Volterra and Fredholm Integral Equations with Smooth Solutions
نویسندگان
چکیده
A spectral collocation method is proposed to solve Volterra or Fredholm integral equations with weakly singular kernels and corresponding integro-differential equations by virtue of some identities. For a class of functions that satisfy certain regularity conditions on a bounded domain, we obtain geometric or supergeometric convergence rate for both types of equations. Numerical results confirm our theoretical analysis. Mathematics subject classification: 45G20, 46A16, 46A22, 65M70.
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