Computational and Applied Mathematics

, Volume 37, Issue 4, pp 5187–5202 | Cite as

Compact finite difference relaxation method for chaotic and hyperchaotic initial value systems

  • D. Mathale
  • P. G. Dlamini
  • M. Khumalo


In this paper, we present a new application of higher order compact finite differences to solve nonlinear initial value problems exhibiting chaotic behaviour. The method involves dividing the domain of the problem into multiple sub-domains, with each sub-domain integrated using higher order compact finite difference schemes. The nonlinearity is dealt using a Gauss–Seidel-like relaxation. The method is, therefore, referred to as the multi-domain compact finite difference relaxation method (MD-CFDRM). In this new application, the MD-CFDRM is used to solve famous chaotic systems and hyperchaotic systems. The main advantage of the new approach is that it offers better accuracy on coarser grids which significantly improves the computational speed of the method. The results are compared with spectral-based multi-domain method.


Chaotic and hyperchaotic systems Compact finite differences Multi-domain Relaxation 

Mathematics Subject Classification

65L05 65L12 37M05 


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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of JohannesburgAuckland ParkSouth Africa
  2. 2.Department of Applied Physics and Engineering MathematicsUniversity of JohannesburgJohannesburgSouth Africa
  3. 3.Department of Mathematical SciencesUniversity of South AfricaFloridaSouth Africa

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