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A discrete sequential predictor-corrector regularization method for the solution of ill-posed Volterra equations based on affine continuation into the future interval is presented. An infinite dimensional analogue is derived and analyzed. Stability estimates and convergence in the cases of exact and noisy data are proved. A convergence rate result is proved for finitely smoothing kernels if the exact solution is $\mathcal{C}^{1,\alpha}$-smooth. Numerical examples are presented. The results are compared to other standard regularization methods.

A First-Order Sequential Predictor-Corrector Regularization Method for Ill-Posed Volterra Equations