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This talk looks into NDSolve in some detail. Problems arising from the numerical solution of ordinary differential equations will be explored, including higher order and systems of equations, initial and boundary-value problems, and stiffness. The current state of the numerical solver for partial differential equations is outlined. The discretizations that are used and the current limits are also discussed. Along the way, the various types of errors that inevitably arise are highlighted. These include local, global, spatial, and temporal errors, and examples are used to explain how they can be controlled.
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