Partial Differential Equations

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

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 »