NUMERICAL INTEGRATION DEVICE FOR IMPROPER INTEGRAL

摘要

PURPOSE:To enable integration with high accuracy at high speed by generating a prescribed pseudo source point against the required source point of a specific function F on a surface element S and approximately integrating the prescribed spherical coordinates of this point and converting it to a required variable. CONSTITUTION:To a source point Xs to be a cause to the singularity of the peculiar function F on the surface element S for a curved surface, etc., in a three-didmensional space, a pseudo singular point X's, which is not on the element S, is generated in proximity to this Xs to project the element S to a polygon anti S on a tangential plane in the point Xs approximately. A polar coordinate system (rho,theta) of the point X's centering arround the point Xs is introduced on this polygon anti S loose or eliminate the pseudo-singularity caused by the point X's by the variable change in the direction of a radius vector. Next, when performing the integration in the direction of the variable, the high-speed improper integral is performed approximately with high accuracy.