Abstract
Novel developments in modern computers have simplified the application of mathematical methods for modeling and simulation of physical phenomena. Continuum mechanics is one of the most popular ways for simulating micro- and nanostructures that do not require computational equipment such as molecular dynamics. Moreover, their results are more accurate compared to simple approaches. However, continuum mechanics usually leads to highly-nonlinear differential equations so that a precise solution cannot be found for them. In this chapter, a variety of numerical approaches to solve the nonlinear differential equations are introduced, and the behavior of some micro- and nanostructures are investigated according to these methods.
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