In this thesis, the existence and uniqueness of solutions for second-kind mixed Volterra-Fredholm integral equations are investigated. Projection-based numerical methods are presented, which consist of two iterative projection algorithms capable of providing accurate approximations to the solution of the given integral equation. For each algorithm, absolute errors and approximate solutions are computed, and their errors are analyzed. Moreover, theoretical error bounds are established and verified through several numerical examples to confirm the accuracy, efficiency, and simplicity of the proposed algorithms for solving second-kind mixed Volterra?Fredholm integral equations.
