Highly accurate two parameter CAGE parallel algorithms for non-linear singular two point boundary value problems

Abstract

We report on highly accurate two parameter coupled alternating group explicit (CAGE) and Newton-CAGE algorithms for the solution of non-linear two point boundary value problems. The proposed algorithms are applicable for both singular and non-singular problems and are suitable for use on parallel computers. The error analysis of the proposed CAGE method is discussed in detail. Computational results are provided to demonstrate the superiority of proposed CAGE and Newton-CAGE iterative methods over the corresponding successive over-relaxation (SOR) and Newton-SOR iterative methods.

Keywords:

• CAGE method
• Newton-CAGE method
• Singular equation
• Two parameter
• Fourth-order method
• Convection–diffusion equation
• Burgers' equation
• RMS errors

Acknowledgements

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