Numerical solution of Volterra–Fredholm integral equations using parameterized pseudospectral integration matrices

The main purpose of this work is to provide parameterized pseudospectral integration matrices (PPIMs) for solving Volterra–Fredholm integral equations. We present an exact, efficient, and stable approach for computing PPIMs. Furthermore, we provide a rigorous convergence analysis for the pseudospectral scheme with collocation at the Jacobi-type points in both L∞ and Lω(α,β)2 spaces. Numerical results confirm the spectral rate of convergence for the proposed pseudospectral schemes.