Abstract
PurposeThis paper deals with the use of the combined Adomian/Alienor methods for solving the problem of optimal cancer chemotherapy model.Design/methodology/approachThe combination of the Adomian decomposition method and the Alienor reducing transformation method allows us to solve the control problem as if it were a classical one dimensional minimization problem. The mathematical model used here describes specific model based on cell‐cycle kinetics.FindingsIt was found that the goal is to maintain the number of the cancerous cells around a desired value while keeping the toxicity to the normal tissues acceptable.Practical implicationsSimulation results are given for illustration.Originality/valueNew combined approach to optimal control of cancer chemotherapy using Adomian/Alienor Methods.
Subject
Computer Science (miscellaneous),Social Sciences (miscellaneous),Theoretical Computer Science,Control and Systems Engineering,Engineering (miscellaneous)
Reference13 articles.
1. Abbaoui, K., Cherruault, Y. and N'Dour, M.N. (1995), “The decomposition method applied to differential systems”, Kybernetes, Vol. 24 No. 8, pp. 32‐40.
2. Cherruault, Y. (1989), “Convergence of Adomian's method”, Kybernetes, Vol. 18 No. 2, pp. 31‐8.
3. Cherruault, Y. (1998), Modèles et méthodes mathématiques pour les sciences du vivant, Presses Universitaires de France (PUF), Paris.
4. Cherruault, Y. (1999), Optimisation, Méthodes Locales et Globales, Presses Universitaires de France (PUF), Paris.
5. Cherruault, Y. and Adomian, G. (1993), “Decomposition method: a new proof of convergence”, Mathl. Comput. Modelling, Vol. 18 No. 12, pp. 103‐6.