New quadrature and Haar wavelet for numerical simulation of real definite and improper integral

Abstract

A new quadrature scheme is designed in this paper to find approximate solution of real definite and improper integral. The proposed rule inbreeds Gauss Legendre 3-point and 5-point Fejer’s second rule to form mixed rule for single and double variables. Convergence analysis is illustrated. Five test problems are executed and compared with results obtained by Haar wavelet and exact solution to test robustness and applicability of the current method. The efficiency and less functional evaluation are main advantage of the suggested rule.