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The analysis of singular perturbed di?erential equations began early in the twentieth century, when approximate solutions were constructed from asy- totic expansions. (Preliminary attempts appear in the nineteenth century - see vD94].)Thistechniquehas?ourishedsincethemid-1960sanditsprincipal ideas and methods are described in several textbooks; nevertheless, asy- totic expansions may be impossible to construct or may fail to simplify the given problem and then numerical approximations are often the only option. Thesystematicstudyofnumericalmethodsforsingularperturbationpr- lems started...

The analysis of singular perturbed di?erential equations began early in the twentieth century, when approximate solutions were constructed from asy- totic expansions. (Preliminary attempts appear in the nineteenth century see vD94].)Thistechniquehas?ourishedsincethemid-1960sanditsprincipal ideas and methods are described in several textbooks; nevertheless, asy- totic expansions may be impossible to construct or may fail to simplify the given problem and then numerical approximations are often the only option. Thesystematicstudyofnumericalmethodsforsingularperturbationpr- lems started somewhat...

An easy-to-understand guide covering the key principles of finite element methods and its applications to differential equations.