6TH-ORDER RUNGE-KUTTA FORWARD-BACKWARD SWEEP ALGORITHM FOR SOLVING OPTIMAL CONTROL MODELS OF EPIDEMIOLOGICAL TYPE
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Abstract
This paper seeks to formulate a more accurate forward-backward algorithm for solving optimal control
problems using the 7-stage Runge-Kutta of order 6 (RK6) numerical scheme. The control variable were
approximated using the interpolating polynomial or spine while the RK6 forward and backward sweeps
were used in approximating the state and adjoint variables respectively because its A-stability, accuracy
and higher rate of convergence. Three numerical examples were simulated to ascertain the accuracy and
convergence of the 6th order Runge-Kutta forward-backward sweep method (K6FBSM). It was
discovered that the RK6FBSM performs better when compared with the Euler and the 4th order Runge-
Kutta Forward-Backward Sweep method RK4FBSM.
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