A new design of mathematical model of therapeutic compound in blood flow patterns in a capillary attached the magnetic nanoparticles by the external magnetic field which is applied uniformly is considered. The blood flowing through the capillary is dominated to be Newtonian and the flow is assumed unsteady, incompressible and laminar. Based on the present knowledge of the drug delivery, the mathematical models have highly potential to develop by researchers. The implementation of the sequential algorithm is used to model the magnetic nanoparticles drug delivery system. Discretization of the governing equation together with the boundary condition is carried out before they are solved numerically using a finite difference scheme. The sequential algorithms on the mathematical model based on some numerical methods such as Jacobi and Gauss Seidel. The numerical analysis investigates in terms of execution time, accuracy, computational complexity, convergence criterion, root means square error and maximum error. The Gauss Seidel is the superior method compared to Jacobi.