Numerical solution of optimal control of atherosclerosis using direct and indirect methods with shooting/collocation approach

We present a direct numerical method for the solution of an optimal control problem controlling growth LDL (Low-density Lipoprotein), HDL (High-density Lipoprotein) and plaque. The is constrained with system coupled nonlinear free mixed boundary partial differential equations consisting three parabolics one elliptic ordinary equations. In first step, original transformed from into fixed condition to Neumann one. Then, employing point-collocation method, we solve problem. each step point iteration, changed linear then, are solved using collocation bringing about NLP which sequential quadratic programming. obtained verified indirect methods originating first-order optimality conditions. Numerical results considered illustrate efficiency methods.