TL;DRAbstract
The vast majority of differential equations that arise as models for real physical systems cannot be solved directly by analytical methods. Often, the only way to proceed is to use a computer to calculate an approximate, numerical solution. However, if one or more small, dimensionless parameters appear in the differential equation, it may be possible to use an asymptotic method to obtain an approximate solution. Moreover, the presence of a small parameter often leads to a singular perturbation problem, which can be difficult, if not impossible, to solve numerically.
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The vast majority of differential equations that arise as models for real physical systems cannot be solved directly by analytical methods. Often, the only way to proceed is to use a computer to calculate an approximate, numerical solution. However, if one or more small, dimensionless parameters appear in the differential equation, it may be possible to use an asymptotic method to obtain an approximate solution. Moreover, the presence of a small parameter often leads to a singular perturbation problem, which can be difficult, if not impossible, to solve numerically.
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