Approximate solutions of nonlinear two‐dimensional Volterra integral equations

Abstract

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.

Hybridization of Block-Pulse and Taylor Polynomials for Approximating 2D Fractional Volterra Integral Equations

“…Wang et al [33] applied the modified block-by-block technique, while Mohammad et al [36] proposed an efficient approach based on Framelets for solving the 2DFVIEs. Ahsan et al [37] used optimal Homotopy asymptotic scheme and Fazeli et al [38] considered the Chebyshev polynomials for approximating the 2DFVIEs. Laib et al [39] applied a numerical approach based on Taylor polynomials for the 2DFVIEs.…”