| Citation: |
Lorand Gabriel Parajdi, Flavius Pătrulescu, Radu Precup, Ioan Ştefan Haplea. TWO NUMERICAL METHODS FOR SOLVING A NONLINEAR SYSTEM OF INTEGRAL EQUATIONS OF MIXED VOLTERRA-FREDHOLM TYPE ARISING FROM A CONTROL PROBLEM RELATED TO LEUKEMIA[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 1797-1812. doi: 10.11948/20220197
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TWO NUMERICAL METHODS FOR SOLVING A NONLINEAR SYSTEM OF INTEGRAL EQUATIONS OF MIXED VOLTERRA-FREDHOLM TYPE ARISING FROM A CONTROL PROBLEM RELATED TO LEUKEMIA
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Abstract
The aim of this paper is to present two algorithms for numerical solving of a fixed final state control problem in connection with the leukemia treatment strategy. In the absence of the controllability condition, our model leads to a nonlinear integral system of Volterra type to whom explicit iterative techniques apply and converge. Once using the controllability condition, the control variable is expressed in terms of the state variables and the integral system changes to a mixed Volterra-Fredholm type one making direct iterative techniques inoperative. However, two paths can be followed. One consists in an iterative procedure where at each step the control variable is calculated using the approximate values of the state variables from the previous step. The other looks for the numerical value of the control variable by using the bisection method. Numerical simulations, error analysis and biological interpretation are given.
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References
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Lorand Gabriel Parajdi, Flavius Pătrulescu, Radu Precup, Ioan Ştefan Haplea. TWO NUMERICAL METHODS FOR SOLVING A NONLINEAR SYSTEM OF INTEGRAL EQUATIONS OF MIXED VOLTERRA-FREDHOLM TYPE ARISING FROM A CONTROL PROBLEM RELATED TO LEUKEMIA[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 1797-1812. doi: 10.11948/20220197
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Figure 1.
Graph of
$ u $ $ v_T\in\{11.11, 14.01, 15.61\} $ -
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$ v $ $ v_T\in\{11.11, 14.01, 15.61\} $ -
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$ 46 $ $ v_T $ $ 11.11 $ $ 15.61 $ -
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