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We demonstrate an efficient numerical method for the solution of partial differential equations arising from a model suggested by BROCAS and CHERRUAULT and completed by CHERRUAULT and GUILLEZ.

The object of this study is a comparison of two minimization methods (“Aliénor” and “Vignes directe”) applied to the mathematical modelization of a biological system, viz. the ventilatory system. “Aliénor's method” is a new global optimization technique which is not very often used, while “Vignes directe's method” has already existed for a long time.

The major challenge for the peri-urban agriculture in the South is to maintain the food supply of cities because the food chains are often local and made up of a number of humble actors: Families seek out their living from small parcels of land, farmers sell directly to consumers, on street markets, or deliver their crops to small collectors who in turn sell to retailers. This differs greatly with the North where food chains provision societies through hyper- and supermarkets and are linked to large producers. Moreover, such chains use modern transportation and preservation systems and they are global. Similar technological and social advancement can also be observed today in the South. Consequently, a social turmoil forces out rural growers from the traditional chains can be observed; as a result, they become city dwellers and engage in urban food production.

This article deals with the significant transformations of agriculture observed in cities of the South, namely: i) changes in the organisation of the food industry in relation to the scale of transactions ii) the role of agriculture in the process of becoming a city-dweller and iii) the emergence of the multi-functionality of agriculture based on a new city-agriculture relationship. Observations are based on the doctoral dissertations of Ba (2007) and To (2008).