A number of physical problems can be described by a complex differential equation with an undetermined coefficient appearing as an explicit term. The problem is usually encountered in diffusion-reaction systems and in these cases the unknown parameter is the gradient at the diffusing interface. The problem is stiff and difficult to solve. This paper describes a new method for the solution of such problems. The procedure is based on the boundary integral element concepts where both the dependent variable and its gradient become the primary variables. This permits a direct iterative solution to this problem. Numerical studies presented here show that the proposed solution method is very accurate and rapidly convergent. Two cases studies involving gas absorption with chemical reaction are also presented.