Partial Differential Equations

Partial Differential Equations in Mathematica 11

Mathematica Version 11 adds extensive support for symbolic solutions of boundary value problems related to classical and modern PDEs. Numerical PDE-solving capabilities have been enhanced to include events, sensitivity computation, new types of boundary conditions, and better complex-valued PDE solutions. These developments provide powerful and flexible tools for modeling problems in physics, engineering, and other fields.

Key Features

  • Symbolically solve boundary value problems for the classical PDEs. »
  • Obtain symbolic solutions for the Schrödinger and other modern PDEs.
  • Solve initial and boundary value problems for general linear PDEs.
  • Find complete solutions for Sturm-Liouville problems related to ODEs.
  • Numerically solve PDEs with periodic boundary conditions over regions. »
  • Numerically solve PDEs over regions with events. »
  • Interactively solve numerical PDEs.
  • Compute numerical sensitivities of PDEs over regions. »

Related Examples

Solve an Initial Value Problem for the Wave Equation »

Solve an Initial Value Problem for the Heat Equation »

Solve a Dirichlet Problem for the Laplace Equation »

Solve a Dirichlet Problem for the Helmholtz Equation »

Solve a Basic Sturm–Liouville Problem »

Solve a Sturm–Liouville Problem for the Airy Equation »

Solve an Initial-Boundary Value Problem for a First-Order PDE »

Solve an Initial Value Problem for a Linear Hyperbolic System »

Solve PDEs with Complex-Valued Boundary Conditions over a Region »

Solve PDEs with Events over Regions »

Interactively Solve and Visualize PDEs »

Solve a Poisson Equation with Periodic Boundary Conditions »

Analyze a Sturm–Liouville Operator with an Asymmetric Potential »

Solve a Wave Equation with Absorbing Boundary Conditions »

Solve a Wave Equation with Periodic Boundary Conditions »

Solve a Poisson Equation in a Cuboid with Periodic Boundary Conditions »

Study the Vibrations of a Stretched String »

Model the Flow of Heat in an Insulated Bar »

Study Dispersion in Quantum Mechanics »

Observe a Quantum Particle in a Box »

Generate Oscillations in a Circular Membrane »

Study the Formation of a Shock Wave »

Find the Value of a European Call Option »

Construct a Complex Analytic Function »