Efficient Finite Difference Discretizations of Partial Differential Operators

JuliaDiffEq is the most popular github organization for solving differential equations in Julia.Currently, it has an assorted collection of Ordinary Differential Equations (ODE), StochasticDifferential Equations (SDE) and Algebraic Differential Equations (DAE) solvers.

But currently, there is no support for Partial Differential Equations (PDEs) which form an integral class of Differential equations found ubiquitously in natural sciences and engineering. PDEs are generally solved approximately by discretizing them to form ODEs which can then be solved separately.

A toolbox to solve a large family of scientifically-interesting PDEs is thus sought. In light of this, I propose to create a toolbox of methods for discretizing PDEs in Julia.