The solving linear one-dimemsional Volterra integral equations of the second kind in reproducing kernel space

Solving integral equations of the third kind in the reproducing kernel space

A reproducing kernel Hilbert space restricts the space of functions to smooth functions and has structure for function approximation and some aspects in learning theory. In this paper, the solution of an integral equation of the third kind is constructed analytically using a new method. The analytical solution is represented in the form of series in the reproducing kernel space. Some numerical ...

solving integral equations of the third kind in the reproducing kernel space

a reproducing kernel hilbert space restricts the space of functions to smooth functions and has structure for function approximation and some aspects in learning theory. in this paper, the solution of an integral equation of the third kind is constructed analytically using a new method. the analytical solution is represented in the form of series in the reproducing kernel space. some numerical ...

A New Approach for Solving Volterra Integral Equations Using The Reproducing Kernel ‎Method

This paper is concerned with a technique for solving Volterra integral equations in the reproducing kernel Hilbert space. In contrast with the conventional reproducing kernel method, the Gram-Schmidt process is omitted here and satisfactory results are obtained.The analytical solution is represented in the form of series.An iterative method is given to obtain the approximate solution.The conver...

Monte Carlo Simulation to Solve the Linear Volterra Integral Equations of The Second Kind

This paper is intended to provide a numerical algorithm based on random sampling for solving the linear Volterra integral equations of the second kind. This method is a Monte Carlo (MC) method based on the simulation of a continuous Markov chain. To illustrate the usefulness of this technique we apply it to a test problem. Numerical results are performed in order to show the efficiency and accu...

Degenerate kernel approximation method for solving Hammerstein system of Fredholm integral equations of the second kind

Degenerate kernel approximation method is generalized to solve Hammerstein system of Fredholm integral equations of the second kind. This method approximates the system of integral equations by constructing degenerate kernel approximations and then the problem is reduced to the solution of a system of algebraic equations. Convergence analysis is investigated and on some test problems, the propo...

Numerical Solution of Fuzzy Linear Volterra Integral Equations of the Second Kind by Homotopy Analysis Method