Multiple-scale perturbation method on integro-differential equations: Application to continuous-time quantum walks on regular networks in non-Markovian reservoirs

An improvement to the homotopy perturbation method for solving integro-differential equations

On the application of homotopy perturbation method to differential equations

We show that a recent application of homotopy perturbation method to a class of ordinary differential equations yields either useless or wrong results. There has recently been great interest in the application of several approximate procedures, like the homotopy perturbation method (HPM), the Adomian decomposition method (ADM), and the variation iteration method (VIM), to a variety of linear an...

Application of He’s Homotopy Perturbation Method and Variational Iteration Method for Nonlinear Partial Integro-differential Equations

In the research, nonlinear volterra partial integro-differential equation is considered. This paper compares the Homotopy Perturbation Method (HPM) with Variational Iteration Method (VIM) for solving this equation. Compared with the Adomian Decomposition Method (ADM), the methods used for this equation need less work. The results of applying these methods show the simplicity and efficiency of t...

New Iterative Method: Application to nth-Order Integro-Differential Equations

In the present article, we implement the new iterative method with a reliable algorithm to solve the nth-order linear/ nonlinear integro-differential equations. The obtained results confirm the power of the method in reducing the size of calculations compared with the other methods.

Coherent transport on Apollonian networks and continuous-time quantum walks.

We study the coherent exciton transport on Apollonian networks generated by simple iterative rules. The coherent exciton dynamics is modeled by continuous-time quantum walks and we calculate the transition probabilities between two nodes of the networks. We find that the transport depends on the initial nodes of the excitation. For networks up to the second generation the coherent transport sho...