Abstract:

In this paper, a new algorithm for solving the second Volterra type integral equation is proposed by combining the least square method with the reproducing kernel method. By constructing the multi-scale orthogonal basis of the reproducing kernel space, the solution expression of the model is obtained. To reduce the amount of computation and simplify the calculation process, this paper transforms the model into linear algebraic equation by using least square method and obtains the approximate solution of $\varepsilon$. In addition, to verify the rigor of the algorithm, the uniform convergence and stability of the algorithm are proved in detail, and the error estimation is discussed and analyzed. The feasibility and applicability of the proposed algorithm are verified by numerical examples. Compared with some known methods, the results obtained in this paper are more accurate.

Key words: Least square method, Reproducing kernel space, Volterra integral equation