• CAPD

  • Referenced in 44 articles [sw07620]
  • flexible C++ modules designed for rigorous numerics in dynamical systems. The CAPD library...
  • RedHom

  • Referenced in 12 articles [sw08776]
  • programs. RedHom originated from research in rigorous numerics of dynamical systems based on topological methods...
  • galepu

  • Referenced in 7 articles [sw15103]
  • this paper, we introduce a constructive rigorous numerical method to compute smooth manifolds implicitly defined...
  • sapa

  • Referenced in 66 articles [sw11944]
  • index. The software used to produce the numerical examples has been made available ... literature as an intermediate text between more rigorous mathematically-oriented texts and practically-oriented engineering...
  • INTOPT_90

  • Referenced in 294 articles [sw04705]
  • book as indicated by the term “rigorous” in the title. That means that for each ... pages) features a rather practical and numerical approach in a branch and bound pattern touching...
  • VNODE

  • Referenced in 16 articles [sw11946]
  • VNODE, Validated Numerical ODE, is a C++ package for computing rigorous bounds on the solution...
  • SLICOT

  • Referenced in 71 articles [sw01095]
  • error or warning indicator; 3. numerical stability and accuracy: the results are as good ... standardisation: the library is based on rigorous programming and documentation standards; 7. benchmarking...
  • Chaste

  • Referenced in 33 articles [sw00122]
  • been subject to a far more rigorous testing procedure than that is usual in this ... incorporated into Chaste. Whiteley has developed a numerical algorithm for solving the bidomain equations that...
  • CkAnalytic

  • Referenced in 5 articles [sw19313]
  • used to obtain mathematically rigorous error bounds on numerical approximations of solutions of differential equations...
  • DODGSON

  • Referenced in 12 articles [sw12653]
  • provide numereous explicit evaluations of determinants. They were all conjectured, and then rigorously proved...
  • Eldarica

  • Referenced in 2 articles [sw09748]
  • verification toolkit for numerical transition systems. This paper presents a publicly available toolkit ... benchmark suite for rigorous verification of Integer Numerical Transition Systems (INTS), which can be viewed ... infrastructure is a starting point for rigorous benchmarking, competitions, and standardized communication between tools...
  • SAGE Interacts

  • Referenced in 1 article [sw19392]
  • accessible without delving into the mathematical rigor of numerical methods. The author illustrates the benefits...
  • na10

  • Referenced in 42 articles [sw11511]
  • Numerical computation of polynomial zeros by means of Aberth’s method. n algorithm for computing ... suitable stop condition, based on a rigorous backward rounding error analysis, guarantees that the computed ... presented together with the results of the numerical tests performed...
  • Algorithm 838

  • Referenced in 12 articles [sw04464]
  • negative real axis. The computational methods are numerical integration of the differential equation and summation ... adaptable to any precision, and amenable to rigorous error analysis. The module can be used...
  • IntervalArithmetic.jl

  • Referenced in 1 article [sw29043]
  • IntervalArithmetic.jl: Rigorous oating-point calculations using interval arithmetic in Julia. IntervalArithmetic.jl ... Julia package for performing Validated Numerics in Julia, i.e. rigorous computations with finite-precision floating...
  • MMM2D

  • Referenced in 4 articles [sw18357]
  • evaluated. Rigorous error bounds for the energies and the forces are derived and numerically verified...
  • JOREK

  • Referenced in 6 articles [sw13477]
  • Energy conservation and numerical stability for the reduced MHD models of the non-linear JOREK ... code. In this paper we present a rigorous derivation of the reduced MHD models with ... more robust especially with respect to numerical errors in the saturation phase of an instability...
  • iRNA-PseColl

  • Referenced in 28 articles [sw24441]
  • modifications, which are essential for numerous biological processes. Knowledge about the occurrence sites ... density distribution of its constituent nucleotides. Rigorous cross-validations have indicated that the anticipated success...
  • FEMVib

  • Referenced in 1 article [sw09266]
  • take advantage of existing numerical libraries. FEMVib has been rigorously tested to resolve the eigenvalues...
  • Lorenz-Database

  • Referenced in 5 articles [sw14477]
  • database of rigorous and high-precision periodic orbits of the Lorenz model. A benchmark database ... very high-precision numerical and validated initial conditions of periodic orbits for the Lorenz model...