A new reproducing kernel method with higher convergence order for solving a Volterra–Fredholm integral equation

In the paper, linear Volterra–Fredholm integral equations of the second kind are considered in a reproducing kernel space. The approximate solution is gotten by constructing a uniquely solvable system of linear algebraic equations. Our important contributions are to provide convergence order theorems of the scheme using spline function theories and propose a new scheme with high convergence order for solving the approximate solutions to oscillation and non-oscillation of exact solutions.