On the application of the SMAGE parallel algorithms on a non-uniform mesh for the solution of non-linear two-point boundary value problems with singularity

Abstract

In this paper, we report on a non-uniform mesh smart alternating group explicit (SMAGE) parallel algorithm for the solution of non-linear singular two-point boundary value (BV) problems. The proposed method requires three non-uniform grid points and is applicable to both singular and non-singular problems. We also discuss the Newton-SMAGE parallel algorithm for the non-linear difference equations. The error analysis of the method is discussed and numerical tests are performed to demonstrate the utility of the proposed SMAGE iterative methods.

Keywords:

• Non-uniform mesh
• SMAGE method
• Newton-SMAGE method
• Singular equation
• Convection–diffusion equation
• Burgers' equation

Acknowledgements

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