home
Home
Modeling Languages
    ModelingToolkitCatalystNBodySimulatorParameterizedFunctionsProcessSimulatorMomentClosure
Model Libraries and Importers
    ModelingToolkitStandardLibraryModelingToolkitNeuralNetsDiffEqCallbacksFiniteStateProjectionCellMLToolkitSBMLToolkitBaseModelicaAudioPluginsReactionNetworkImportersDiffEqPhysicsDiffEqFinancialPubChemPyomoMathML
Symbolic Tools
    ModelOrderReductionSymbolicsSymbolicUtilsSymbolicIntegrationSymbolicSMTSymbolicLimitsSymbolicAnalysisFunctionProperties
Array Libraries
    RecursiveArrayToolsComponentArraysLabelledArraysMultiScaleArrays
Equation Solvers
    LinearSolveNonlinearSolveDifferentialEquationsIntegralsDifferenceEquationsOptimizationJumpProcessesLineSearchEvolutionaryNeuralLinearSolveCorleone
Inverse Problems / Estimation
    CurveFitSciMLSensitivityDiffEqParamEstimDiffEqBayes
PDE Solvers
    MethodOfLinesNeuralPDENeuralOperatorsFEniCSHighDimPDEDiffEqOperatorsFiniteVolumeMethodFiniteVolumeMethod1DPDEBase
Advanced Solver APIs
    OrdinaryDiffEqBoundaryValueDiffEqDiffEqGPUSteadyStateDiffEqOrdinaryDiffEqOperatorSplittingIRKGaussLegendreMATLABDiffEqQuantumNLDiffEq
Parameter Analysis
    EasyModelAnalysisGlobalSensitivityStructuralIdentifiabilityMinimallyDisruptiveCurvesCatalystNetworkAnalysis
Third-Party Parameter Analysis
    BifurcationKit
Uncertainty Quantification
    PolyChaosSciMLExpectationsOptimalUncertaintyQuantification
Function Approximation
    SurrogatesReservoirComputing
Implicit Layer Deep Learning
    DiffEqFluxDeepEquilibriumNetworksNeuralLyapunov
Symbolic Learning
    DataDrivenDiffEqSymbolicNumericIntegration
Third-Party Differentiation Tooling
    SparseDiffToolsFiniteDiff
Numerical Utilities
    ExponentialUtilitiesDiffEqNoiseProcessPreallocationToolsEllipsisNotationDataInterpolationsDataInterpolationsNDPoissonRandomQuasiMonteCarloRuntimeGeneratedFunctionsMuladdMacroFindFirstFunctionsSparseDiffToolsBipartiteGraphsFastAlmostBandedMatricesFastBroadcastFunctionWrappersWrappersLHLFactorizationLightweightStatsPureGebalPureKLUPureUMFPACKRootedTreesSparseBandedMatricesRespecializeParamsConcreteStructs
High-Level Interfaces
    SciMLBaseSciMLStructuresSciMLLoggingADTypesSymbolicIndexingInterfaceTermInterfaceSciMLOperatorsSurrogatesBaseCommonSolveSciMLIteratorsStatic
Third-Party Interfaces
    ArrayInterfaceStaticArrayInterface
Developer Documentation
    SciMLStyleColPracDiffEq Developer DocumentationOrgMaintenanceScripts
Extra Resources
    SciMLWorkshopExtended SciML TutorialsThe SciML BenchmarksModelingToolkitCourse
Commercial Support
    JuliaHub logo - contact sales today!

    JuliaHub offers commercial support for ModelingToolkit and the SciML ecosystem. Contact us today to discuss your needs!
Products built with SciML
  • Dyad
  • Pumas
  • Cedar EDA
  • Neuroblox
  • Planting Space
    /
    MethodOfLines.jl logo
    MethodOfLines.jl
    • MethodOfLines.jl: Automated Finite Difference for Physics-Informed Learning
    • Tutorials
      • Getting Started
      • Solving the Heat Equation
      • Resolving Steep Gradients: WENO on Non-Uniform Grids
      • Showcase: Resolving Interfacial Gradients with Non-Uniform WENO
      • Adding parameters
      • Learning a missing term with a neural network
      • Learning the Brusselator reaction with a neural network
      • Learning the Brusselator reaction in two dimensions
      • Steady State Heat Equation - No Time Dependence - NonlinearProblem
      • Steady state of SIS (suspected-infected-suspected) reaction-diffusion model
      • Initial and Boundary Conditions with sampled/measured Data
      • Solving PIDEs (Integrals)
      • Schrödinger Equation
    • MOLFiniteDifference
    • PseudospectralDiscretization
    • Solution Interface - PDESolutions
    • Grid and Solution Retrieval - Deprecated
    • Boundary Conditions
    • Advection Schemes
    • Non-Uniform Rectilinear Grids
    • Curvilinear Grids
    • FAQs
    • How it Works
    • Notes for Developers: Implement a Scheme
    • Generated Examples
      • Generated Code for the Brusselator Equation
      • Generated ODE system for the Brusselator Equation
    • API Reference
      • Discretization
      • Utilities
    Version
    • API Reference
    • Utilities
    • Utilities
    GitHub

    Utilities

    The utility functions used by the discretization interfaces are documented in the public API and developer API reference sections.

    « Discretization

    Powered by Documenter.jl and the Julia Programming Language.

    Settings


    This document was generated with Documenter.jl version 1.19.0 on Wednesday 16 September 2026. Using Julia version 1.13.0.