Partial Differential Equation Toolbox User’s Guide (R2025a)

Solve PDE Problems Inside MATLAB R2025a

Partial differential equations underpin much of modern engineering analysis, from heat flow and structural stress to electromagnetic fields. The Partial Differential Equation Toolbox User’s Guide is MathWorks’ official R2025a reference for working with these equations in MATLAB. It is a practical, release-specific manual for setting up PDE models, choosing the right workflow, and moving from geometry to mesh to numerical solution without leaving the MATLAB environment.

What the Guide Covers

The guide begins with the toolbox product description, the equations you can solve, and the unified modeling workflow. It then walks through the essential building blocks of a finite element model:

• Creating and importing 2-D and 3-D geometry, including polygons, triangulated meshes, and primitive shapes such as cuboids, cylinders, and spheres
• Generating and assessing mesh quality, with tools for finding elements and nodes by location
• Specifying PDE coefficients, initial conditions, and boundary conditions, including Dirichlet, Neumann, and mixed conditions
• Solving static, dynamic, thermal, electromagnetic, and structural problems
• Visualizing results and working with reduced-order models for faster analysis

A Workflow Built Around PDEModel Objects

Much of the guide centers on the unified PDEModel workflow, which allows you to define a problem step by step and keep geometry, mesh, coefficients, boundary conditions, and solution data together. This approach supports both command-line scripting and the PDE Modeler app, making it possible to switch between interactive exploration and reproducible code. The material also covers migration from older domain-specific workflows, which is useful for engineers updating existing scripts to current MATLAB practices.

Examples Across Engineering Disciplines

Rather than staying abstract, the user’s guide includes numerous worked examples that show the toolbox in context. You will find models such as von Mises stress and displacements in the PDE Modeler app, deflection of a piezoelectric actuator, dynamics of a damped cantilever beam, thermal stress analysis of a jet engine turbine blade, finite element analysis of an electrostatically actuated MEMS device, magnetic flux density in an H-shaped magnet, and heat transfer in an orthotropic material plate due to a laser beam. These examples span structural mechanics, heat transfer, electromagnetics, and coupled multiphysics, giving readers concrete patterns they can adapt to their own simulations.

Who This Guide Is For

This manual is written for engineers, scientists, researchers, and advanced MATLAB users who need to solve partial differential equations numerically. If you are new to the toolbox, the early chapters provide the conceptual grounding and workflow overview needed to get started. If you already use the toolbox, the R2025a edition serves as a current function reference and a source of updated examples, including migration guidance and reduced-order modeling techniques.

Why the R2025a Edition Matters

MATLAB releases evolve, and documentation must keep pace. The R2025a edition reflects the toolbox as it stands in Version 25.1, with updated coverage of the unified workflow, geometry and mesh handling, boundary condition specification, and solution visualization. For anyone maintaining models or developing new ones, using release-matched documentation helps avoid mismatches between examples and the functions available in the current installation.

Practical Reference for Computational PDE Work

Keep this guide nearby when you are setting up a new model, troubleshooting boundary conditions, or looking for a worked example that resembles your own problem. It is a thorough, official companion to the Partial Differential Equation Toolbox, and its digital format makes it easy to search, copy function names, and follow along while you work in MATLAB.