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A free-boundary problem involving an elliptic partial differential equation is one in which some part of the boundary is not known in advance, but is to be determined so that some extra boundary condition is satisfied. In some relevant iterative methods instabilities may retard or inhibit convergence, and here these difficulties are avoided by a generalization of the Regula-Falsi method, whose use is standard for the determination of a zero of a function of one variable. An example, involving axi-symmetric incompressible cavitational flow past a circular disk placed coaxially inside a cylinder, successfully illustrates the method.

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