Abstract
We propose and apply coupling of the variational iteration method (VIM) and homotopy perturbation method (HPM) to solve nonlinear mixed Volterra-Fredholm integrodifferential equations (VFIDE). In this approach, we use a new formula called variational homotopy perturbation method (VHPM) and variational accelerated homotopy perturbation method (VAHPM). This approach is based on the form of He’s polynomials and on a new form of He’s polynomials. We discuss the convergence of the technique. Some numerical examples are introduced to verify the efficiency of this technique.
Highlights
There has been a clear interest in integrodifferential equations which are a combination of differential and Volterra-Fredholm integral equations
Integrodifferential equations play an important role in many branches of linear and nonlinear functional analyses and their applications
Rabbani and Kiasoltani [5] studied the solving of a nonlinear system of Volterra-Fredholm integrodifferential equations (VFIDE) by using the discrete collocation method
Summary
There has been a clear interest in integrodifferential equations which are a combination of differential and Volterra-Fredholm integral equations. The mentioned integrodifferential equations are usually difficult to solve analytically, so approximation strategies are required to obtain the solution of the linear and nonlinear integrodifferential equations [1]. Al-Jubory [3] introduced some approximation methods to solve Volterra-Fredholm integral and integrodifferential equations. HPM has been applied with great success, so relations and algorithms have been deduced and continuously improved to obtain an accurate solution for a large variety of linear and nonlinear problems. He in [7] used a strategy to solve some integrodifferential equations where he chose an initial approximate solution in the form of an exact solution with unknown constants. A new approach based on VIM with HPM is introduced to solve the two-dimensional nonlinear VFIDE
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