A Hermite based block method (HBBM) is proposed for the numerical solution of second-order non-linear
elliptic partial differential equations (PDEs). The development of the method was accomplished through the
methodology of interpolation and collocation procedures. The method’s analysis reveals that it satisfied the
requirements for a numerical technique to be convergent. The implementation of the method is extensively
discussed. Five numerical examples originating from physical phenomena are presented, and the applicability
and accuracy of the HBBM are established by comparing them with the existing methods; the haar wavelet
collocation method, the modified cubic B-spline collocation method, and the modified decomposition method.
The proposed methods of HBBM are more accurate, stable, and convergent