xSPDE: extensible Stochastic Partial Differential Equations

Peter D. Drummond, Simon Kiesewetter

xSPDE was developed at the Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Victoria, Australia.

Thanks for much valuable feedback and many useful suggestions from: Bogdan Opanchuk, Rodney Polkinghorne, Simon Kiesewetter, Laura Rosales-Zarate, King Ng and Run Yan Teh.

• Introduction to xSPDE
• Interactive xSPDE
  • Stochastic equations
  • Interactive examples
  • Ito and Stratonovich equations
  • Stochastic partial differential equations
• Averaging and projects
  • Using xsim and xgraph
  • Ensembles in xSPDE
  • xSPDE projects
  • Data files and batch jobs
  • Sequential integration
  • xSPDE hints
• Tutorial
  • Wiener process
  • Harmonic oscillator
  • Kubo oscillator
  • Soliton
  • Gaussian with HDF5 files
  • Planar noise
  • Extensible simulations
  • Characteristic
  • Equilibrium
• xSIM
  • How xSIM works
  • Averaged data
  • Stochastic flowchart
  • Data arrays and ensembles
  • Coordinates, integrals and derivatives
  • Interaction picture and Fourier transforms
  • Fields
• xGRAPH
  • Input and data arrays
  • Customization options
  • Graphics functions
  • Sequenced observables: data
• Algorithms
  • Notation
  • xSPDE algorithms
  • Euler
  • Second order Runge-Kutta
  • Midpoint
  • Fourth order Runge-Kutta
  • Convergence checks
  • Extrapolation order and error bars
  • Sampling errors
• Public API
  • High-level xSPDE functions and objects
  • Low-level xSPDE functions
  • Input parameters and user functions
  • xSIM functions
  • xGRAPH parameters
  • xGRAPH functions
  • Parameter structure
  • Default functions
  • Frequently asked questions
• References

Indices and tables

• Index
• Module Index
• Search Page