This book reviews and compares some well-known numerical methods and more recent contributions for solving both moving boundary and boundary value problems. Recent advances in the finite difference solution of linear and non-linear partial differential equations are also presented and algorithmic manipulations which enhance the computational efficiency are incorporated into the overall schemes. This can be applied to many physical problems involving the heat or diffusion equations in fluid mechanics and heat transfer of the WKB-type slow variation complex wave equation in electromagnetism and solid state physics. The book treats the subject from an engineering point of view. It introduces new numerical methods and compares them with other methods in terms of not only accuracy but also computational efficiency.
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