This is the second of a pair of papers describing the use of boundary tracing for boundary value problems. In the preceding article, the theory of the technique was explained and it was shown how it enables one to use known exact solutions of partial differential equations to generate new solutions. Here, we illustrate the use of the technique by applying it to three equations of practical significance: Helmholtz's equation, Poisson's equation and the nonlinear constant mean curvature equation. A variety of new solutions are obtained and the potential of the technique for further application outlined.
|Journal||Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences|
|Publication status||Published - 2007|