Boundary Integral Equation Solution of Non-linear Plane Potential Problems

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Abstract
This paper presents the boundary integral equation (BIE) formulation, and numerical solution procedure for two-dimensional problems governed by Laplac's equation and subject to non-linear boundary conditions. The introduction of non-linear terms constitutes a fundamental extension of the BIE method, as previous applications have been restricted entirely to linear problems. Furthermore, non-linearities necessitate the use of iterative solution techniques which present the conceptual disadvantage that a solution is not guaranteed. However, such difficulties were not encountered with the Newton—Raphson method employed in this study. The various features of the BIE technique are illustrated by the application to a physical problem which is of significance in heat exchanger design.

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