Approximate Solution of Real Definite Integrals in Adaptive Routine

Abstract

A mixed quadrature rule of higher precision has been formulated by taking two constituent rules each of lower degree of precision. Mixed quadrature rule in adaptive environment is used for evaluation of real definite integrals over a circle or triangle which is best fit to the Fracture Mechanics. Mixed quadrature rules have been applied in various fields of Science and Technology. Objectives: Mixed quadrature rule has become a milestone in the field of Science and Technology. Methods/Statistical Analysis: A mixed quadrature rule of degree of precision nine has been formed by taking two constituent rules each of degree of precision seven. Findings: The mixed quadrature rule has been tested in adaptive routine and it has found to be more effective than that of Clenshaw-curtis seven-point rule. Application: Mixed quadrature rule in adaptive environment is used for evaluation of real definite integral over a circle or triangle which is best fit to the fracture mechanics.