# The Variational Iteration Method for Solving Asymmetric System of PDEs

## TL;DR

This paper introduces a generalized variational iteration method to solve asymmetric systems of PDEs, ensuring unique solutions and applying it to fluid flow problems.

## Contribution

It extends the He variational iteration method to asymmetric PDE systems and guarantees solution uniqueness using Banach fixed point theorem.

## Key findings

- Iterative schemes for fluid flow systems are developed.
- The method guarantees unique solutions for asymmetric PDEs.
- Applications to incompressible fluid flow demonstrate effectiveness.

## Abstract

We propose a method to obtain iterative schemes guarantee unique solutions for systems of partial differential equations that are not symmetric with respect to the time by generalizing He variational iteration method and using Banach fixed point theorem. Then, iterative schemes for systems of incompressible fluid flow and incompressible micropolar fluid flow will be created by applying the generalized He variational iteration method.