Improvement in the numerical method for integrating weight function of pre-cracked specimen

• Gauss Chebyshev–Richardson method has been proposed for integrating weight function.
• The proposed method yields convergence in less iteration than Gauss Chebyshev method.
• Romberg–Richardson method is more efficient than the proposed method.

This paper introduces modification in the existing Gauss–Chebyshev method for computation of stress intensity factor in a pre-cracked specimen. Richardson extrapolation method has been introduced for modification of Gauss–Chebyshev method and the modified method is named as Gauss–Chebyshev–Richardson method. The Gauss–Chebyshev–Richardson method yields more accurate solution after a few numbers of iterations than the method in its original form. Also, Romberg–Richardson method, recently introduced by the authors, has been used to compare the results. To this end, a comparative study of the results obtained using Gauss–Chebyshev method, Romberg method, Romberg–Richardson method and Gauss–Chebyshev–Richardson method has been presented.