Fourth-order accurate BLAGE iterative method for the solution of two-dimensional elliptic equations in polar co-ordinates

Abstract

In this article, we report on the block alternating group explicit (BLAGE) iterative method for solving the block symmetric linear system derived from the fourth-order accurate nine-point discretisation of a two-dimensional elliptic equation in cylindrical polar co-ordinates. The error analysis of the BLAGE method is discussed briefly. The performance of this more accurate BLAGE method is compared with the corresponding block successive over relaxation (BSOR) method by considering two test problems, wherein the significance of the role played by two parameters ω₁ and ω₂ of the BLAGE method becomes evident in providing both convergence and accuracy of the computed solution.

Keywords:

• Elliptic equation
• Polar cylindrical co-ordinates
• Fourth-order scheme
• Tri-diagonal solver
• BLAGE iterative method
• RMS errors

Acknowledgement

This research was supported by ‘The Royal Society’ of London, UK under INSA Bilateral Indo-UK Joint Exchange Programme.