Discrete collocation method for solving two-dimensional linear and nonlinear fuzzy Volterra integral equations

Abstract

This paper proposes a discrete collocation method based on the fuzzy Lagrange interpolation and the fuzzy Gauss-Legendre quadrature formula for solving two-dimensional linear and nonlinear fuzzy Volterra integral equations. Firstly, the existence and uniqueness of the solution of the original equation are proved by using a two-dimensional Gronwall inequality and an iterative method. Secondly, the discrete collocation method is utilized to convert the linear and nonlinear fuzzy Volterra integral equations into the corresponding linear and nonlinear systems of algebraic equations. Finally, the error estimation and convergence analysis of the proposed numerical method are discussed in terms of the uniform modulus of continuity. Some numerical experiments illustrate that the scheme possesses a higher accuracy and yields a better approximation when compared with other known methods.