Solving nonlinear integral equations in the Urysohn form by Newton–Kantorovich–quadrature method

Solving nonlinear integral equations in the Urysohn form by Newton-Kantorovich-quadrature method

A Numerical Method for Solving Nonlinear Integral Equations

In this paper, an iterative scheme based on the homotopy analysis method (HAM) has been used to solve nonlinear integral equations. To check the numerical method, it is applied to solve different test problems with known exact solutions and the numerical solutions obtained confirm the validity of the numerical method and suggest that it is an interesting and viable alternative to existing numer...

A Method for Solving Nonlinear Volterra Integral Equations

It is known that to construct the stable multistep method with the higher order of accuracy for solving integral equation is actual. For this aim here we suggest some ways for the construction of hybrid methods for solving nonlinear Volterra integral equations of the second kind. Thus, foundational this extends stable hybrid method with higher order of accuracy. Note that the hybrid methods whi...

Wilson wavelets for solving nonlinear stochastic integral equations

A new computational method based on Wilson wavelets is proposed for solving a class of nonlinear stochastic It^{o}-Volterra integral equations. To do this a new stochastic operational matrix of It^{o} integration for Wilson wavelets is obtained. Block pulse functions (BPFs) and collocation method are used to generate a process to forming this matrix. Using these basis functions and their operat...

Convergence of Legendre wavelet collocation method for solving nonlinear Stratonovich Volterra integral equations

In this paper, we apply Legendre wavelet collocation method to obtain the approximate solution of nonlinear Stratonovich Volterra integral equations. The main advantage of this method is that Legendre wavelet has orthogonality property and therefore coefficients of expansion are easily calculated. By using this method, the solution of nonlinear Stratonovich Volterra integral equation reduces to...