In this paper, we propose the triangular orthogonal functions as a basis functions
 for solution of weakly singular Volterra integral equations second
 kind. Powerful properties these and some operational matrices
 are utilized in direct method to reduce equation to
 algebraic equations. The presented does not need any integration
 obtaining constant coefficients. is co...

‎A natural algorithm with an optimal order of convergence is proposed for numerical solution of a class of cordial weakly singular Volterra integral equations‎. ‎The equations of this class appear in heat conduction problems with mixed boundary conditions‎. ‎The algorithm is based on a representation of the solution and compound Gaussian quadrature rules with graded meshes‎. ‎A comparative stud...

A symmetric spectral method is applied to investigate the two-dimensional Volterra integral equation with weakly singular kernels and delays. In this work, solution of we considered assumed be sufficiently smooth so that can naturally. Employing three couples variable transformations, apply Gauss quadrature rule approximate delays obtain discretization. Then derive convergence results proposed ...

In this paper, we propose and analyze a spectral approximation for the numerical solutions of fractional integro-differential equations with weakly kernels. First, original are transformed into an equivalent singular Volterra integral equation, which possesses nonsmooth solutions. To eliminate singularity solution, introduce some suitable smoothing transformations, then use Jacobi collocation m...

Bernstein polynomials have been recently used for the solution of some linear and non-linear differential equations, both partial and ordinary, by Bhatta and Bhatti [1] and Bhatti and Bracken [2]. Also these have been used to solve some classes of inegral equations of both first and second kinds, by Mandal and Bhattacharya [3]. These were further used to solve a Cauchy singular integro-differen...