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 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 »
