In this letter, the numerical scheme of nonlinear Volterra-Fredholm integro-differential equations is proposed in a reproducing kernel Hilbert space (RKHS). The method is constructed based on the reproducing kernel properties in which the initial condition of the problem is satised. The nonlinear terms are replaced by its Taylor series. In this technique, the nonlinear Volterra-Fredholm integro...

in this paper, a numerical solution for a system of linear fredholm integro-differential equations by means of the sinc method is considered. this approximation reduces the system of integro-differential equations to an explicit system of algebraic equations. the exponential convergence rate $o(e^{-k sqrt{n}})$ of the method is proved. the analytical results are illustrated with numerical examp...

In this paper, we propose a method to approximate the solution of a linear Fredholm integro-differential equation by using the Chebyshev wavelet of the first kind as basis. For this purpose, we introduce the first Chebyshev operational matrix of integration. Chebyshev wavelet approximating method is then utilized to reduce the integro-differential equation to a system of algebraic equations. Il...

a computational method for numerical solution of a nonlinear volterra and fredholm integro-differentialequations of fractional order based on chebyshev cardinal functions is introduced. the chebyshev cardinaloperational matrix of fractional derivative is derived and used to transform the main equation to a system ofalgebraic equations. some examples are included to demonstrate the validity and ...

Abstract: In this paper, a numerical method to solve nonlinear Fredholm integral equations of second kind is proposed and some numerical notes about this method are addressed. The method utilizes Chebyshev wavelets constructed on the unit interval as a basis in the Galerkin method. This approach reduces this type of integral equation to solve a nonlinear system of algebraic equation. The method...

We study the parametrized Hamiltonian action functional for finitedimensional families of Hamiltonians. We show that the linearized operator for the L2-gradient lines is Fredholm and surjective, for a generic choice of Hamiltonian and almost complex structure. We also establish the Fredholm property and transversality for generic S1-invariant families of Hamiltonians and almost complex structur...

In this paper, we present a Taylor-series expansion method for a class of Fredholm singular integro-differential equation with Cauchy kernel. This method uses the truncated Taylor-series polynomial of the unknown function and transforms the integro-differential equation into an nth order linear ordinary differential equa.tion with variable coefficients: ~y Galerkin method we use the orthogonal ...

this paper describes an approximating solution, based on lagrange interpolation and spline functions, to treat functional integral equations of fredholm type and volterra type. this method can be extended to functional dierential and integro-dierential equations. for showing eciency of the method we give some numerical examples.

In this work, an algorithm for finding numerical solutions of linear fractional delay-integro-differential equations (LFDIDEs) variable-order (VO) is introduced. The operational matrices are used as discretization technique based on shifted Chebyshev polynomials (SCPs) the first kind with spectral collocation method. proposed VO-LFDIDEs have multiterms integer, fractional-order derivatives dela...