• Octave

  • Referenced in 284 articles [sw00646]
  • integrating ordinary functions, manipulating polynomials, and integrating ordinary differential and differential-algebraic equations...
  • REDUCE

  • Referenced in 739 articles [sw00789]
  • facilities for defining new functions and extending program syntax; analytic differentiation and integration; factorization ... solution of a variety of algebraic equations; facilities for the output of expressions ... calculations with a wide variety of special functions; Dirac matrix calculations of interest to high...
  • gfun

  • Referenced in 132 articles [sw00344]
  • example, given two generating functions defined by linear differential equations with polynomial coefficients, there...
  • INTLAB

  • Referenced in 419 articles [sw04004]
  • optimization) roots of univariate and multivariate nonlinear equations (simple and clusters) eigenvalue problems (simple ... problems (simple and clusters) quadrature for univariate functions univariate polynomial zeros (simple and clusters) interval ... automatic differentiation (forward mode, vectorized computations, fast) Gradients (to solve systems of nonlinear equations) Hessians ... global optimization) Taylor series for univariate functions automatic slopes (sequential approach, slow for many variables...
  • deSolve

  • Referenced in 50 articles [sw04499]
  • algebraic equations (DAE), and delay differential equations (DDE) , Functions that solve initial value problems ... system of first-order ordinary differential equations (ODE), of partial differential equations (PDE), of differential ... equations (DAE), and of delay differential equations. The functions provide an interface to the FORTRAN ... partial differential equations (PDE) that have been converted to ODEs by numerical differencing...
  • DOLFIN

  • Referenced in 161 articles [sw04313]
  • FEniCS. A large part of the functionality of FEniCS is implemented as part of DOLFIN ... based on partial differential equations and implements core parts of the functionality of FEniCS, including...
  • ode23

  • Referenced in 279 articles [sw06600]
  • integrates the system of differential equations y′ = f(t,y) from time ... first input argument, odefun, is a function handle. The function, f = odefun...
  • INTOPT_90

  • Referenced in 304 articles [sw04705]
  • equations and optimization. Preprint.). The chapter about non-differentiable problems (17 pages) studies function expressions...
  • DIMSYM

  • Referenced in 72 articles [sw04279]
  • solve linear partial differential equations. To use its primary function the user specifies a system ... ordinary and/or partial differential equations and the type of symmetry to be found (Lie point...
  • Chebfun

  • Referenced in 327 articles [sw05897]
  • involving numbers to continuous or piecewise-continuous functions. It also implements continuous analogues of linear ... solves ordinary differential equations. The mathematical basis of the system combines tools of Chebyshev expansions...
  • diffEq

  • Referenced in 35 articles [sw11101]
  • Functions from the book Solving Differential Equations in R. Functions and examples from the book...
  • PDESpecialSolutions

  • Referenced in 62 articles [sw12342]
  • exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs. Algorithms are presented ... solutions of nonlinear ordinary and partial differential equations (ODEs and PDEs). New algorithms are given ... parameters so that the differential equations admit polynomial solutions in tanh, sech, combinations thereof, Jacobi ... compute exact solutions of nonlinear differential equations...
  • COMSOL

  • Referenced in 367 articles [sw04091]
  • boundary conditions can all be arbitrary functions of the dependent variables.Predefined multiphysics-application templates solve ... specify your own partial differential equations (PDEs) and link them with other equations and physics...
  • bvp4c

  • Referenced in 233 articles [sw06178]
  • solinit) integrates a system of ordinary differential equations of the form ... odefun and bcfun are function handles. See the function_handle reference page for more information...
  • HolonomicFunctions

  • Referenced in 45 articles [sw06666]
  • differential equations, linear recurrences, q-difference equations, and mixed linear equations that a given function ... creative telescoping. As subtasks, the following functionalities have been implemented in HolonomicFunctions: computations ... difference-differential operators), noncommutative Gröbner bases, and solving of coupled linear systems of differential ... difference equations...
  • Mittag-Leffler

  • Referenced in 74 articles [sw12626]
  • called generalized exponential function). The Mittag-Leffler function with two parameters plays an important role ... appears frequently in solutions of fractional differential equations (i.e. differential equations containing fractional derivatives...
  • Maxima

  • Referenced in 151 articles [sw00560]
  • series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, and sets, lists, vectors ... precision floating point numbers. Maxima can plot functions and data in two and three dimensions...
  • Green

  • Referenced in 28 articles [sw09355]
  • Green’s Functions in the Theory of Ordinary Differential Equations.- Appendix A. A Green...