An accurate spline polynomial cubature formula for double integration with logarithmic singularity - Bichi S.L.; Eshkuvatov Z.K.; Long N.M.A.N.; Bello M.Y. (American Institute of Physics Inc., 2024)
The paper studied the integration of logarithmic singularity problem J(y)=???(y)log|y-y0?|dA, where y=(?,?), y0=(?0,?0) the domain ? is rectangle ? = [r1, r2] [r3, r4], the arbitrary point y? and the fixed point y0?. The given density function ?(y), is smooth on the rectangular domain ? and is in the functions class C2,? (?). Cubature formula (CF) for double integration with logarithmic singularities (LS) on a rectangle ? is constructed by applying type (0, 2) modified spline function D?(P). The results obtained by testing the density functions ?(y) as linear and absolute value functions shows that the constructed CF is highly accurate. 2016 Author(s).