Solving two-dimensional nonlinear fuzzy Volterra integral equations by homotopy analysis method

• Main Author: Georgieva Atanaska
• Format: Article
• Language: English
• Published: De Gruyter 2021-04-01
• Series: Demonstratio Mathematica
• Subjects: homotopy analysis method; two-dimensional nonlinear fuzzy volterra integral equation; convergence; error estimation; 41a25; 45g10; 65r20
• Online Access: https://doi.org/10.1515/dema-2021-0005

The purpose of the paper is to find an approximate solution of the two-dimensional nonlinear fuzzy Volterra integral equation, as homotopy analysis method (HAM) is applied. Studied equation is converted to a nonlinear system of Volterra integral equations in a crisp case. Using HAM we find approximate solution of this system and hence obtain an approximation for the fuzzy solution of the nonlinear fuzzy Volterra integral equation. The convergence of the proposed method is proved. An error estimate between the exact and the approximate solution is found. The validity and applicability of the HAM are illustrated by a numerical example.