The basin of Timgad belongs to the North-Eastern Algerian Saharan Atlas; it is located at the northern extension of the Aures Mountains. The basin is an asymmetrical syncline oriented East-West covering an area of 1000 Km2. The climate is semi-arid (cold winter and hot summer) with average annual rainfall not exceeding 400 mm. Recently, the increasing agricultural activities led to an excessive exploitation of groundwater resources. In order to meet this rising water supply demands, implementing a water resources management policy is a priority which should be based on a basin hydrogeological study. Effectively, the geological and geophysical studies have confirmed the presence of permeable Miocene and Cretaceous formations (sandstone and carbonate); relatively resistant affected by fractures network, which are probably forming a confined aquifers. Indeed, recent wells drilled in the basin center and their boundaries; show that the aquifers are artesian. The sandstone aquifer of the Miocene is the most important, it is characterized by significant thickness which can exceed 200m, its extension as well as its particular corrugated geometry, characterized by a wavy shape, which forming a series of shale-marl filling depressions, influences the groundwater flow, actually, the piezometric surface illustrates groundwater convergent flow oriented to the east, towards Bou el freis, likewise the sandstone aquifer is marked by the presence of a West-East drainage axis which separates the basin northern part characterized by a low reservoirs hydraulic capacity from the southern part distinguished by the groundwater relative abundance. Groundwater is generally easily extracted, except the northern part of the basin where the top shale-marl layer is thickens to over 1000m.

The basin of Timgad belongs to the North-Eastern Algerian Saharan Atlas; it is located at the northern extension of the Aures Mountains. The basin is an asymmetrical syncline oriented East-West covering an area of 1000 Km2. The climate is semi-arid (cold winter and hot summer) with average annual rainfall not exceeding 400 mm. Recently, the increasing agricultural activities led to an excessive exploitation of groundwater resources. In order to meet this rising water supply demands, implementing a water resources management policy is a priority which should be based on a basin hydrogeological study. Effectively, the geological and geophysical studies have confirmed the presence of permeable Miocene and Cretaceous formations (sandstone and carbonate); relatively resistant affected by fractures network, which are probably forming a confined aquifers. Indeed, recent wells drilled in the basin center and their boundaries; show that the aquifers are artesian. The sandstone aquifer of the Miocene is the most important, it is characterized by significant thickness which can exceed 200m, its extension as well as its particular corrugated geometry, characterized by a wavy shape, which forming a series of shale-marl filling depressions, influences the groundwater flow, actually, the piezometric surface illustrates groundwater convergent flow oriented to the east, towards Bou el freis, likewise the sandstone aquifer is marked by the presence of a West-East drainage axis which separates the basin northern part characterized by a low reservoirs hydraulic capacity from the southern part distinguished by the groundwater relative abundance. Groundwater is generally easily extracted, except the northern part of the basin where the top shale-marl layer is thickens to over 1000m.

In this paper, we present some our ongoing researches related to a collocation method based on a double projection scheme via regularization procedure, to numerically solve Cauchy integral equations of the second kind. For the collocation approach, we use spline quasi-interpolating projectors of degree $d$. We prove the existence of the solution for a double projection scheme. Moreover, we give new error bounds.