Integro-differential invariants of one-parameter groups of Fredholm transformations

Solving Non-linear Fredholm Integro-differential Equations

In this paper, Semi-orthogonal (SO) B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of linear and non-linear second order Fredholm integro-differential equations. The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this functions are presented to reduce the solution of linear and...

Interpolation correction for collocation solutions of Fredholm integro-differential equations

In this paper we discuss the collocation method for a large class of Fredholm linear integro-differential equations. It will be shown that, when a certain higher order interpolation operation is added to the collocation solution of this equation, the new approximations will, under suitable assumptions, admit a multiterm error expansion in even powers of the step-size h. Based on this expansion,...

Numerical Solution of Fredholm Integro-differential Equations By Using Hybrid Function Operational Matrix of ‎Differentiation‎

In this paper‎, ‎first‎, ‎a numerical method is presented for solving a class of linear Fredholm integro-differential equation‎. ‎The operational matrix of derivative is obtained by introducing hybrid third kind Chebyshev polynomials and Block-pulse functions‎. ‎The application of the proposed operational matrix with tau method is then utilized to transform the integro-differential equations to...

USING PG ELEMENTS FOR SOLVING FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

In this paper, we use Petrov-Galerkin elements such as continuous and discontinuous Lagrange-type k-0 elements and Hermite-type 3-1 elements to find an approximate solution for linear Fredholm integro-differential equations on $[0,1]$. Also we show the efficiency of this method by some numerical examples  

Legendre-Galerkin method for the linear Fredholm integro-differential equations