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Neway, if anybody knows of any good articlkes that i could read that would be great. Do ppl still use eulers and runge kutta's methods? thanx. Really appreciate it. !1

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- Thread starter mooberrymarz
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- #1

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Neway, if anybody knows of any good articlkes that i could read that would be great. Do ppl still use eulers and runge kutta's methods? thanx. Really appreciate it. !1

- #2

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I think there is a trend towards using boundary element methods over finite difference or finite element methods. This means you turn your differential equation into an integral equation and solve that instead. For a long time people liked FEM and FDM because they generated sparse matrices which are easy to solve, as opposed to BEM which ALWAYS generate dense matrices. But now there are fast-solvers and better computers which can handle dense matrices much easier, so BEM are becoming more practical.

Advantages of BEM are that you can solve exterior problems 'exactly', whereas the other methods require some sort of truncation of your mesh. Also, BEM often converge spectrally (exponentially), which is much faster than the average FE method. The downside to them is that it's sometimes difficult/impossible to turn the differential equation into an integral equation.

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