1-D Partial Differential Equations

1-D solver for parabolic and elliptic PDEs

Partial differential equations contain partial derivatives of functions that depend on several variables. MATLAB^® lets you solve parabolic and elliptic PDEs for a function of time and one spatial variable. For more information, see Solving Partial Differential Equations.

Partial Differential Equation Toolbox™ extends this functionality to problems in 2-D and 3-D with Dirichlet and Neumann boundary conditions.

Plotted solutions of two 1-D partial differential equation problems

Functions

`pdepe`	Solve 1-D parabolic and elliptic PDEs
`odeget`	Extract ODE option values
`odeset`	Create or modify options structure for ODE and PDE solvers
`pdeval`	Interpolate numerical solution of PDE

Topics

Solving Partial Differential Equations
Solve 1-D partial differential equations with pdepe.
Solve Single PDE
This example shows how to formulate, compute, and plot the solution to a single PDE.
Solve PDE with Discontinuity
This example shows how to solve a PDE that interfaces with a material.
Solve PDE and Compute Partial Derivatives
This example shows how to solve a transistor partial differential equation (PDE) and use the results to obtain partial derivatives that are part of solving a larger problem.
Solve System of PDEs
This example shows how to formulate, compute, and plot the solution to a system of two partial differential equations.
Solve System of PDEs with Initial Condition Step Functions
This example shows how to solve a system of partial differential equations that uses step functions in the initial conditions.

Related Information

Numerical Methods with Applications (MathWorks Teaching Resources)