Mathematics of Computation, Vol. 59, No. 200 (Oct., 1992), pp. 403-420 (18 pages) We apply Runge-Kutta methods to linear partial differential equations of the form u t (x, t) = L (x, ∂)u(x, t) + f(x, ...

Solutions of the n-th order linear ordinary differential equations ${\left( {z + b} \right)^1}\prod\limits_{k = 1}^{n - 1} {\left( {z + {a_k}} \right){\varphi _n ...

Partial differential equations can describe everything from planetary motion to plate tectonics, but they’re notoriously hard to solve. Unless you’re a physicist or an engineer, there really isn’t ...

Read article at Massey Research Online: In deformations of material objects, physical laws give the final state minimising an energy functional and solving a typically non-linear partial differential ...

Sometimes, it’s easy for a computer to predict the future. Simple phenomena, such as how sap flows down a tree trunk, are straightforward and can be captured in a few lines of code using what ...