Abstract：For the difficulty to determine the integral range and the integral function, the constraint quadrilateral method for calculating a partition convolution is proposed. The constraint relationship between independent variable t and integral dummy variable τ of the two segment functions in a being calculated convolution is a constraint quadrilateral domain in τ-t coordinate system. By drawing straight lines perpendicular to the axis t through the quadrilateral vertices, convolution segments and quadrilateral subdomains about independent variable t can be defined, furthermore, by drawing arrows parallel to axis between adjacent lines in each subdomain, the integral paths, integrands and limits of integration can be represented clearly. Thus, the analytical formula of a convolution in each subdomain can be attained by adding all convolution integrals in the subdomain.Furthermore, formulas for calculating the number of constraint quadrilateral and convolution segments are also developed. Example results show that this method is simple and effective for convolution calculation.

Keyword：constraint quadrilateral;partition convolution;integral path;integrand;limits of integration;