• FEniCS

  • Referenced in 856 articles [sw04314]
  • efficient solution of differential equations, including automated solution of variational problems, automated error control...
  • UFL

  • Referenced in 77 articles [sw11183]
  • equations with a view to numerical approximation. Features of UFL include support for variational forms ... methods for complex systems of partial differential equations in near-mathematical notation, resulting in compact ... library generates abstract syntax tree representations of variational problems, which are used by other software...
  • VFGEN

  • Referenced in 14 articles [sw00995]
  • single definition of the user’s equations, VFGEN can generate code for initial value problem ... extending a vector field with its variational equation, converting delay equations to finite dimensional approximations...
  • Aghora

  • Referenced in 12 articles [sw13971]
  • Stokes equations coupled with turbulence transport equations, variational multi-scale formulation of large-eddy simulation...
  • ERATO

  • Referenced in 39 articles [sw11922]
  • calculated by linearizing the ideal MHD equations. Any mode (unstable or stable) of the spectrum ... Solution method: The variational form of the 2D ideal MHD equations is treated...
  • MERLIN

  • Referenced in 14 articles [sw04248]
  • refer to systems of non-linear equations, to variational methods, to curve fitting...
  • D3M

  • Referenced in 11 articles [sw42185]
  • based on the variational principle is proposed for partial differential equations (PDEs). The solution ... proposed framework establishes a foundation to use variational deep learning in large-scale engineering problems...
  • D-NURBS

  • Referenced in 17 articles [sw09123]
  • nonlinear differential equations, produces physically meaningful, and hence intuitive shape variation. Consequently, a modeler ... Lagrangian mechanics to formulate the equations of motion for D-NURBS curves, tensor-product...
  • ParMooN

  • Referenced in 14 articles [sw16810]
  • instationary Navier-Stokes equations, turbulent flows using large eddy simulation and variational multiscale methods ... surfactants, flows with deforming moving/structures, coupled scalar equations and population balance equations...
  • MAP

  • Referenced in 7 articles [sw11471]
  • wise schemes for hyperbolic conservative equations. The total variation diminishing (TVD) limiters and approximate Riemann ... extended generalized Lagrange multiplier (EGLM) MHD equations to reduce the non-divergence free error produced...
  • Breach

  • Referenced in 26 articles [sw20822]
  • differential equations that can also provide information about sensitivity with respect to parameters variation...
  • DifferentialGeometry

  • Referenced in 30 articles [sw07593]
  • groups, transformation groups, jet spaces, and the variational calculus. These capabilities, combined with dramatic recent ... symbolic approaches to solving algebraic and differential equations, have allowed for development of powerful...
  • 4D-VAR

  • Referenced in 13 articles [sw03477]
  • linearization, or adjoint equation, or minimization process in comparison with variational schemes, but nevertheless...
  • WHFast

  • Referenced in 2 articles [sw34178]
  • symplectic tangent map for the variational equations. This allows us to efficiently calculate two widely...
  • KEPLER

  • Referenced in 2 articles [sw08618]
  • other methods, to the integration of variational equations. For the Kepler problem, the space...
  • VarNet

  • Referenced in 9 articles [sw42184]
  • VarNet: Variational Neural Networks for the Solution of Partial Differential Equations. In this paper ... VarNet, for the solution of partial differential equations (PDEs) using deep neural networks (NNs). Particularly ... novel loss function that relies on the variational (integral) form of PDEs as apposed...
  • OpenOpticalFlow

  • Referenced in 3 articles [sw38423]
  • including the physics-based optical flow equation, the variational solution, and errors. The central part...
  • Modulef

  • Referenced in 39 articles [sw01072]
  • time-dependent thermal problems and dynamic problems; variational inequalities; Solution of the Dirichlet problem ... viscous incompressible fluid (Navier-Stokes equations). Computation of homogenised coefficients of composite structures. Decomposition...
  • Elvet

  • Referenced in 1 article [sw39550]
  • Elvet - a neural network-based differential equation and variational problem solver. We present Elvet ... Python package for solving differential equations and variational problems using machine learning methods. Elvet ... system of coupled ordinary or partial differential equations with arbitrary initial and boundary conditions...
  • BayesPy

  • Referenced in 3 articles [sw15438]
  • tedious task of implementing the variational Bayesian update equations, the user can construct models faster ... advanced methods such as stochastic and collapsed variational inference...