Node averaged nodal integral method

In this paper, a new variant of the nodal integral method (NIM) is proposed for the solution of 2D diffusion equation. In NIM, the scheme is derived using Transverse Integration Process (TIP) and analytical solutions of ODEs within nodes. This analytical pre-processing dramatically improve the quality of the solution, which is the main distinguishing feature of NIM. However, in this new approach, the TIP is performed at node center instead of node edge. Adapting this approach simplifies the scheme and make it easier to solve. To test the capabilities of this newly developed scheme, some benchmark problems using the diffusion equation are solved. It is found that the scheme is as accurate as traditional NIM, and the scheme is relatively easy to solve. It can be said that a simplified scheme is developed while retaining the accuracy of traditional NIM.