PDE and Applied Mathematics Seminar[ Edit ]
Moderator: Amy Novick-Cohen
Typically, when semi-discrete approximations to time-dependent partial differential equations (PDE) or explicit multistep schemes for ordinary differential equation (ODE) are constructed they are derived such that they are stable and have a specified truncation error $\tau$. Under these conditions, the Lax--Richtmyer equivalence theorem assures that the scheme converges and that the error is, at most, of the order of $||\tau||$. In most cases, the error is in indeed of the order of $||\tau||$.
We demonstrate that schemes can be constructed, whose truncation errors are $\tau$, however, the actual errors are much smaller. This error reduction is done by constructing the schemes such that they inhibit the accumulation of the local errors, therefore they are called Error Inhibiting Schemes (EIS).
ADI DITKOWSKI, School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel. email: email@example.com