On the numerical solution of nonlinear Volterra-Fredholm integral equations by collocation methods
SIAM Journal on Numerical Analysis
Asymptotic expansion for the trapezoidal Nystro¨m method of linear Volterra-Fredholm equations
Journal of Computational and Applied Mathematics
A reliable treatment for mixed Volterra-Fredholm integral equations
Applied Mathematics and Computation
Homotopy perturbation method: a new nonlinear analytical technique
Applied Mathematics and Computation
A fast iterative method for discretized Volterra-Fredholm integral equations
Journal of Computational and Applied Mathematics
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The purpose of this paper is to obtain the approximation solution of the strongly nonlinear mixed Volterra-Fredholm integral equation (VFIE). For some strongly nonlinear problems, the traditional homotopy perturbation method is divergent, so we propose a modified homotopy perturbation method which is still convergent when solving the strongly nonlinear mixed VFIE. By means of this method, an algorithm is successfully established for solving the strongly nonlinear mixed VFIE. And the convergence of the algorithm is proved strictly. Finally, several examples are presented to illustrate the application of the algorithm.