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Overview
Via this page you obtain the spatial discretisation of a dynamical partial differential equation (PDE) using dynamical systems theory. The technique not only ensures consistency of the discretisation, but remarkably theory ensures the exponentially quick relevance of the discretisation at finite grid spacing h. Theory also suggests the numerical disretisation should have good stability properties on a coarse spatial grid. I use a generalised Burgers' equation as an example:

A companion page discretises coupled PDEs in one space dimension, such as the complex GinzburgLandau equation. Later, I may develop web pages interfacing tools for discretisations in two or more spatial dimensions, forced inhomogeneous PDEs and the discretisation near boundaries.
Submit your PDE for analysis
Fill in the following fields for your PDE and its discretisationassume the dependent field u(x,t) is a function of space x and time t. Use the syntax of Reduce for the algebraic expressions. Values of the fields for the generalised Burgers' equation are listed in the third column as an example.
Wait a minute or two
The analysis may take minutes after submitting. Be patient. Perhaps make a cup of coffee while you wait.I also generate a Matlab function implementing the discretisation for integration by ODE45 or equivalent. I give no guarantee of the performance of the discretisation, only that I have endeavoured to analyse your PDE according to the principles summarised in the supporting theory.
Note: in this approach one must use a wide enough stencil in order to represent nonlinear terms with a large number of derivatives, even if each derivative is relatively low order.
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