A novel adaptive cubature scheme based on a hybrid cubature rule has been developed. In the process, we first construct a hybrid cubature rule taking a suitable convex combination of Simpson’s  cubature rule and Gauss-Legendre 2-point cubature rule. We use this hybrid cubature rule as the base rule to develop the new adaptive cubature scheme. Numerically evaluating some test double integrals, it is seen that this adaptive scheme is a very powerful tool to achieve desired accuracy.

Simpson’s  cubature rule  Gauss-Legendre 2-point cubature rule  hybrid cubature rule  double integral, adaptive cubature scheme.