Comparison of Chebyshev and Legendre polynomials methods for solving two dimensional Volterra - Fredholm integral equations

SOLVING NONLINEAR TWO-DIMENSIONAL VOLTERRA INTEGRAL EQUATIONS OF THE FIRST-KIND USING BIVARIATE SHIFTED LEGENDRE FUNCTIONS

In this paper, a method for finding an approximate solution of a class of two-dimensional nonlinear Volterra integral equations of the first-kind is proposed. This problem is transformedto a nonlinear two-dimensional Volterra integral equation of the second-kind. The properties ofthe bivariate shifted Legendre functions are presented. The operational matrices of integrationtogether with the produ...

Fuzzy bivariate Chebyshev method for solving fuzzy Volterra-Fredholm integral equations

Constructing Two-Dimensional Multi-Wavelet for Solving Two-Dimensional Fredholm Integral Equations

In this paper, a two-dimensional multi-wavelet is constructed in terms of Chebyshev polynomials. The constructed multi-wavelet is an orthonormal basis for space. By discretizing two-dimensional Fredholm integral equation reduce to a algebraic system. The obtained system is solved by the Galerkin method in the subspace of by using two-dimensional multi-wavelet bases. Because the bases of subs...

APPLICATION OF FUZZY EXPANSION METHODS FOR SOLVING FUZZY FREDHOLM- VOLTERRA INTEGRAL EQUATIONS OF THE FIRST KIND

In this paper we intend to offer new numerical methods to solvethe fuzzy Fredholm- Volterra integral equations of the firstkind $(FVFIE-1)$. Some examples are investigated to verify convergence results and to illustrate the efficiently of the methods.  

A Numerical Approach for Solving of Two-Dimensional Linear Fredholm Integral Equations with Boubaker Polynomial Bases

In this paper, a new collocation method, which is based on Boubaker polynomials, is introduced for the approximate solutions of a class of two-dimensional linear Fredholm integral equationsof the second kind. The properties of two-dimensional Boubaker functions are presented. The fundamental matrices of integration with the collocation points are utilized to reduce the solution of the integral ...