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Differential Equations and Related Topics

  • EqWorld, The World of Mathematical Equations.
    Extensive information on ordinary differential, partial differential (mathematical physics), integral, functional, and other mathematical equations. It gives exact solutions and outlines solution methods, includes articles, gives links to math websites, lists books, software, and more.
  • Concepts 2.0.0 CONCEPTS is a C++ class library for solving elliptic partial differential equations (PDEs) numerically.
  • Software Package for Adaptivity, Wavelets & Finite Differences AWFD (Adaptivity, Wavelets & Finite Differences) software package is a C++ class library for wavelet/interpolet-based solvers for PDEs and integral equations.
    Department of Scientific Computing and Numerical Simulation, University of Bonn, Germany
  • Particle codes for 2D Coulombic and screened Coulombic interactions
  • Solvers for homogeneous boundary value problems in interior or exterior multiply connected domains with Dirichlet or Neumann conditions: (Laplace and modified Helmholtz equations)
  • Solvers for inhomogeneous boundary value problems in interior or exterior multiply connected domains with Dirichlet or Neumann conditions: (Poisson and modified Helmholtz equations)
  • A test set for initial value problems in ODEs and DAEs (formerly the well known Amsterdam test set) by the numerical analysis group in Bari (Italy) coordinated by Francesca Mazzia The project is sponsored by the Istituto Nazionale di Alta Matematica-Roma (INdAM) and the University of Bari. The aim is to extend the present test set of challenging problems and to include codes for other important classes of differential equations.
    A steering committee of A. Bellen, J. Cash, E. Hairer, F. Krogh, L. Petzold, B. Simeon, G. Soderlind, D. Trigiante and P.J. van der Houwen has been set up to oversee this project.
    Comments for consideration by the committee can be sent to Francesca Mazzia at the e-mail address (testset@dm.uniba.it).
  • SBVP1.0 a MATLAB code (based on collocation) for the numerical solution of singular boundary value problems for systems of ODEs with a singularity of the first kind. Prof. Dr. Ewa B. Weinmüller, Department of Applied Mathematics and Numerical Analysis, Vienna University of Technology.
  • Mimetic Discretizations of Continuum Mechanics This page provides information about mimetic discretizations of continuum mechanics problems, including problems in fluid mechanics, solid mechanics and electrodynamics. Please send proposed additions to this web site to Stanly Steinberg (stanly@wendouree.org).
  • Fortran codes for the numerical solution of differential equations including those of stiff/delay/differential-algebraic types are available courtesy of Ernst Hairer, Université de Genève.
  • Cactus, Parallel Code for PDEs Cactus is a general, modular, parallel code for solving systems of partial differential equations. The code has been developmented over many years by a large international collaboration of numerical relativity and computational science research groups and can be used to provide a portable platform for solving any system of partial differential equations. The code compiles and runs on a variety of different platforms, from laptops running Linux or NT to clusters of workstations, to large T3Es, with no modifications needing to be made to the application codes. cactusmaint@cactuscode.org
  • Five New Codes for Stiff ODEs and DAEs All of these codes are based on the well known approach defined by Modified Extended Backward Differentiation Formulae. (Including sparse solvers.) J. Cash, Imperial College.
  • DAEPACK is an acronym for Differential-Algebraic Equation Package, however, its scope is not limited to the analysis of DAEs. DAEPACK is a software library consisting of components for performing symbolic and numeric computations on general Fortran-90 models.
  • PseudoPack is a software library for numerical differentiation by pseudospectral methods. ( Prof. Bruno Costa and Prof. Wai Sun Don)
  • FIDISOL/CADSOL "FIDISOL/CADSOL is a program package for the solution of partial differential equations. 2- and 3-dimensional systems of elliptic (stationary) and parabolic (time-dependent) equations can be solved. The boundary conditions may be arbitrary. The solution method is the finite difference method. For the FIDISOL part the solution domain is restricted to be rectangular. For the CADSOL part the domain is body-oriented, i. e. logically rectangular. There are versions with an adaptive grid generation. For CADSOL dividing lines can be prescribed allowing the solution of different partial differential equations in different subdomains or allowing noncontinuous conditions inside the domain." (Dr. Ruediger Weiss, Universitaet Karlsruhe)
  • Ordinary Differential Equations: Fortran Codes (and some C codes) produced for the text Hairer, Norsett and Wanner (1993): Solving Ordinary Differential Equations. Nonstiff Problems. 2nd edition. Springer Series in Comput. Math., vol. 8.
  • Convection-diffusion, Stokes and Oseen codes using SUPG and Multigrid (written in Matlab) by David Silvester (UMIST) and Howard Elman (Maryland).
  • ELLPACK "ELLPACK is a very high level, portable system for solving elliptic boundary value problems. One can solve routine problems by simply writing them down and naming the methods to be used. One can solve harder problems by using the problem solving modules in the flexible ELLPACK framework. The ELLPACK language is an easy-to-learn extension of Fortran: this provides greatly reduced coding for most of the computation, but still allows one to do special processing. ELLPACK incorporates over 50 problem solving modules, including some of the best and most current software in the world. A knowledgeable user can even tailor ELLPACK itself by adding new problem solving or analysis modules. "
  • CLAWPACK - A Software Package for Conservation Laws "Clawpack contains software for solving hyperbolic systems of conservation laws in 1 and 2 space dimensions. "
  • Diffpack project - its goal is "...is to develop a fully object-oriented framework for solution of partial differential equations."
  • DifEqu "...is a program designed for numerically solving ordinary, functional and partial differential equations, difference equations and do many more things. It can be used for solving problems arising in mathematics, physics, chemistry, biology. The program is most useful for teaching, doing research and creating simulation.
  • C*ODE*E : Consortium of ODE Experiments.
    "The goal of the Consortium of ODE Experiments is to share the rapidly growing wealth of computational instruction techniques with as many teachers of differential equations as is possible."
    "If you are interested in introducing computer experiments into your ordinary differential equations course, your first decision might be to choose a DE solving package.
  • LASPack is a package for solving large sparse systems of linear equations like those which arise from discretization of partial differential equations.
  • SLEIGN2 - Sturm-Liouville Problems "The main purpose of SLEIGN2 is to compute eigenvalues, eigenfunctions, and to approximate the continuous spectrum of regular and singular Sturm-Liouville (S-L) problems. "
  • LUGR: Adaptive-grid methods for time-dependent PDEs "LUGR methods are meant for the efficient computation of rapidly varying temporal and spatial solution transitions by automatic local grid adaptation." (Dr J.G. Verwer Dr R.A. Trompert (now at the faculty of Geophysics of the University of Utrecht). trompert@geof.ruu.nl J.G. Blom, CWI, AMsterdam.)
  • A practical introduction to Matlab The tutorial is aimed at students who have not used Matlab before. It explains the basics features of Matlab in some detail, with examples, and points the students to the more advanced features. Mark Gockenbach, Michigan Technological University
  • SOLVING DELAY DIFFERENTIAL EQUATIONS IN MATLAB We have developed a MATLAB program, dde23, that solves delay differential equations with constant delays. It is a very capable solver that is exceptionally easy to use. Included are a tutorial on using dde23, a manuscript containing technical details, and a manuscript and a link about event location. The programs run in Matlab 5.
    L.F. Shampine, Southern Methodist University, lshampin@mail.smu.edu
    S. Thompson, Radford University, thompson@runet.edu