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.