A computational code is developed for the integro-differential equations governing the motion of the centerlines of vortex filaments submerged in a background potential flow. These equations, which are derived from the method of matched asymptotic analysis, include the effect of decaying large-magnitude circumferential and axial velocity components in the vortical cores. Numerical examples are presented to assess the effect of large axial velocity and of nonsimilar initial profiles in vortical cores. The initial configurations of the filaments are chosen so as to fulfill the basic assumption of asymptotic analysis, which is the effective vortical core size is much smaller than all other length scales in the flowfield, e.g., the radius of curvature and interfilament distance. The computations are continued until the basic assumption is no longer valid, that is, when the merging or intersection of filaments have begun. Various types of local or global merging or intersection of filaments are classified and demonstrated by numerical examples.