American Journal of Physics 'Iserles has successfully presented, in a mathematically honest way, all essential topics on numerical methods for differential equations, suitable for advanced ...

Mathematical approaches for numerically solving partial differential equations. The focus will be (a ... to illustrate the broad applicability of numerical methods. Students will be expected to ...

Introductory course on using a range of finite-difference methods to solve initial-value and initial-boundary-value problems involving partial differential equations. The course covers theoretical ...

Topics include methods of solutions for linear and non-linear first order differential equations, linear second order differential equations, higher order linear differential equations, systems of ...

However, for all but the simplest devices these equations are typically too complex to permit closed-form solutions. Numerical methods are thus both essential and powerful for predicting the ...

to name just three – can be described using partial differential equations (PDEs). Apart from a few simple cases, these equations are hard to solve analytically, and sometimes even impossible.