The Wolfram Language has powerful functionality for solving a wide variety of partial differential equations both symbolically and numerically. The symbolic capabilities of the Wolfram Language make it possible to efficiently set up PDE equations expressed as PDE terms that can be used by themselves or used as building blocks for assembling larger PDE components.

For specific physics fields, relevant PDE terms have been packaged as components and augmented with boundary condition functions typically encountered in the field.

Basic Building Blocks

Use partial differential equations of the form

DiffusionPDETerm — model diffusion with

ConvectionPDETerm — model convection with

ReactionPDETerm — model reaction with

SourcePDETerm — model a source with

ConservativeConvectionPDETerm — model conservative convection with

DerivativePDETerm — model a derivative of a term with

DirichletCondition  ▪  NeumannValue  ▪  PeriodicBoundaryCondition

Named Partial Differential Equation Terms

LaplacianPDETerm — model with

PoissonPDEComponent — model with

HelmholtzPDEComponent — model with

WavePDEComponent — model with

SchrodingerPDEComponent — model with

DirichletCondition  ▪  NeumannValue  ▪  PeriodicBoundaryCondition

Acoustic PDE Components »

AcousticPDEComponent — model acoustics in the time or frequency domain

AcousticAbsorbingValue  ▪  AcousticImpedanceValue  ▪  AcousticNormalVelocityValue  ▪  AcousticPressureCondition  ▪  AcousticRadiationValue  ▪  AcousticSoundHardValue  ▪  AcousticSoundSoftCondition

Acoustics in the Time Domain — monograph about modeling acoustics in the time domain

Acoustics in the Frequency Domain — monograph about modeling acoustics in the frequency domain

Electromagnetic PDE Components »

ElectrostaticPDEComponent — model electrostatics

ElectricCurrentPDEComponent — model electric currents

MagnetostaticPDEComponent — model magnetostatics for permanent magnets

MagnetostaticPDEComponent — model quasistatic magnetic fields

ElectricPotentialCondition  ▪  ElectricFluxDensityValue  ▪  ElectricSymmetryValue  ▪  MagneticPotentialCondition  ▪  MagneticFluxDensityValue  ▪  MagneticSymmetryValue

Electromagnetism — overview monograph about modeling electromagnetics

Electrostatics — monograph about modeling electrostatics

Electric Currents — monograph about modeling electric currents

Magnetostatics for Permanent Magnets — monograph about modeling permanent magnets

Quasistatic Magnetic Fields — monograph about modeling quasistatic magnetic fields

Fluid Dynamics PDE Components »

FluidFlowPDEComponent — model fluid flow

Laminar Flow — monograph about modeling laminar fluid flow

Heat Transfer PDE Components »

HeatTransferPDEComponent — model heat transfer

HeatFluxValue  ▪  HeatInsulationValue  ▪  HeatOutflowValue  ▪  HeatRadiationValue  ▪  HeatSymmetryValue  ▪  HeatTemperatureCondition  ▪  HeatTransferValue

Heat Transfer — monograph about modeling heat transfer

Heat Transfer Model Verification — test suite with heat transfer model verification

Mass Transport PDE Components »

MassTransportPDEComponent — model mass transport

MassConcentrationCondition  ▪  MassFluxValue  ▪  MassImpermeableBoundaryValue  ▪  MassOutflowValue  ▪  MassSymmetryValue  ▪  MassTransferValue

Mass Transport — monograph about modeling mass transport

Solid Mechanics PDE Components »

SolidMechanicsPDEComponent — model solid mechanics

SolidMechanicsStrain — computes strain from displacement

SolidMechanicsStress — computes stress from strain

SolidFixedCondition  ▪  SolidDisplacementCondition  ▪  SolidBoundaryLoadValue

Solid Mechanics — monograph about modeling solid mechanics

Hyperelasticity — monograph about modeling hyperelastic material

Solid Mechanics Model Verification — test suite with solid mechanics model verification