Approximate solutions of nonlinear two-dimensional Volterra integral equations

The present work is concerned with examining the Optimal Homotopy Asymptotic Method (OHAM) for linear and nonlinear two-dimensional Volterra integral equations (2D-VIEs). The result obtained by the suggested method for linear 2D-VIEs is compared with the differential transform method, Bernstein polynomial method, and piecewise block-plus method and result of the proposed method for nonlinear 2D-VIEs is compared with 2D differential transform method. The proposed method provides us with efficient and more accurate solutions compared to the other existing methods in the literature.

Automated summary

The study examines the Optimal Homotopy Asymptotic Method (OHAM) for linear and nonlinear two-dimensional Volterra integral equations (2D-VIEs), comparing its results with other existing methods and finding it to provide more efficient and accurate solutions.