Forming a mixed Quadrature rule using an anti-Lobatto four point Quadrature rule

A mixed quadrature rule of higher precision for approximate evaluation of real definite integrals has been constructed using an anti-Lobatto rule. The analytical convergence of the rule has been studied. The relative efficiencies of the mixed quadrature rule has been shown with the help of suitable test integrals. The error bound has been determined asymptotically

Numerical Investigation, Error Analysis and Application of Joint Quadrature Scheme in Physical Sciences

In this work, a joint quadrature for numerical solution of the double integral is presented. This method is based on combining two rules of the same precision level to form a higher level of precision. Numerical results of the present method with a lower level of precision are presented and compared with those performed by the existing high-precision Gauss-Legendre five-point rule in two variables, which has the same functional evaluation. The efficiency of the proposed method is justified with numerical examples. From an application point of view, the determination of the center of gravity is a special consideration for the present scheme. Convergence analysis is demonstrated to validate the current method