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Excerpt from Numerical Solution of Nonlinear Boundary Value Problems Using Reflection In the past, free boundary problems have been attacked by iterative procedures which guess the location of the boundary, solve the rest of the equations, and then improve the guess A more accurate and faster scheme was recently reported by Bloch He incorporates a change of independent variables Via a conformal transformation, simplifying the domain of the solution. Then he solves the transformed differential equation in the new (known) domain, Simultaneously solving for the transformation itself. The result is regarded as a parametrized form of the desired solution. The boundary conditions for the transformation are derived from a steepest descent argument, supplemented by equations serving to establish the free boundary constraint, which in his case expresses continuity of pressure across a fluid-air interface. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

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