A spectral collocation method is proposed to solve Volterra or Predholm 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.
Scopus Subject Areas
- Computational Mathematics
- Collocation method
- Integro-differential equations
- Weakly singular kernel