# 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.

## 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.