is a Mathematica paclet that solves nonlinear integral order partial differential equations using the GERF (generalized exponential rational function) expansion technique. For more info on the method, see 10.1140/epjp/i2018-11984-1. To learn more about the paclet, visit the homepage at Wolfram repository.

Installation

is as easy as running

PacletInstall["Taggar/GERF"]

in your local or cloud notebook. Then, load it with

<<Taggar`GERF`

If you decide to use the paclet for research, kindly consider citing it as follows:

Taggar, N. (2026). GERF: A Mathematica paclet for the generalized exponential rational function method (1.2.1). Zenodo. https://doi.org/10.5281/zenodo.20706333.

Usage

Let

burgers = D[u[x, t], t] + u[x, t] * D[u[x, t], x] - \[Nu] * D[u[x, t], x, x] == 0

be the given equation (this is the Burgers' equation in (1+1)-dimensions). Then, use GERFSolve as follows:

sol = GERFSolve[burgers, u[x, t]]

which returns the following output:

Pick any of these and plot it for appropriate values:

Plot3D[
    u[x, t] /. sol[[3]] /. {(* parameters *)},
    {x, -4, 4}, {t, 0, 4},
    PlotRange -> All
]

A full demonstration is available on the Wolfram repository page of this paclet, see GERFSolve.html.

Version log

Version 1.0.0, on 31 March, 2026 — initial upload.

Version 1.1.0, on 30 May, 2026 — support for fractional ordered equations.

Version 1.2.0, 15 June, 2026 — support for systems of equations.

Version 1.2.1, 24 June, 2026 — additional examples added in documentation, and citation information also added.

Contributions

are welcome.