Coupling Adomian and spectral methods for obtaining a numerical solution of an optimal control problem in cancer research

Abstract

Purpose

To compute an optimal control of non‐linear reaction diffusion equations that are modelling inhibitor problems in the brain.

Design/methodology/approach

A new numerical approach that combines a spectral method in time and the Adomian decomposition method in space. The coupling of these two methods is used to solve an optimal control problem in cancer research.

Findings

The main conclusion is that the numerical approach we have developed leads to a new way for solving such problems.

Research limitations/implications

Focused research on computing control optimal in non‐linear diffusion reaction equations. The main idea that is developed lies in the approximation of the control space in view of the spectral expansion in the Legendre basis.

Practical implications

Through this work we are convinced that one way to derive efficient numerical optimal control is to associate the Legendre expansion in time and Runge Kutta approximation. We expect to obtain general results from optimal control associated with non‐linear parabolic problem in higher dimension.

Originality/value

Coupling of methods provides a numerical solution of an optical control problem in Cancer research.

Citation

Mampassi, B., Saley, B., Somé, B. and Cherruault, Y. (2005), "Coupling Adomian and spectral methods for obtaining a numerical solution of an optimal control problem in cancer research", Kybernetes, Vol. 34 No. 7/8, pp. 1125-1141. https://doi.org/10.1108/03684920510605939