general pdes -凯发k8网页登录

solve general linear and nonlinear pdes for stationary, time-dependent, and eigenvalue problems

you can use partial differential equation toolbox™ to solve linear and nonlinear second-order pdes for stationary, time-dependent, and eigenvalue problems that occur in common applications in engineering and science.

a typical workflow for solving a general pde or a system of pdes includes the following steps:

convert pdes to the form required by partial differential equation toolbox.
create a pde model container specifying the number of equations in your model.
defining 2-d or 3-d geometry and mesh it using triangular and tetrahedral elements with linear or quadratic basis functions.
specify the coefficients, boundary and initial conditions. use function handles to specify non-constant values.
solve and plot the results at nodal locations or interpolate them to custom locations.

contour and colored surface plot on a tilted plane

functions

pde model setup

	create model
	add boundary condition to `pdemodel` container
	specify coefficients in a pde model
	give initial conditions or initial solution
	assemble finite element matrices
	solve pde specified in a pdemodel
	solve pde eigenvalue problem specified in a pdemodel

solutions at nodal and custom locations

	evaluate gradients of pde solutions at arbitrary points
	evaluate flux of pde solution
	interpolate pde solution to arbitrary points

visualization

	plot solution or mesh for 2-d problem
	plot solution or surface mesh for 3-d problem
	plot pde geometry
	plot pde mesh
	create and plot pde visualization object

pde model properties

	find boundary condition assignment for a geometric region
	locate active pde coefficients
	locate active initial conditions

legacy workflow

	create solution object
	interpolate data to selected locations
	interpolant for nodal data to selected locations

live editor tasks

create and explore visualizations of pde results in the live editor

objects

	pde model object
	time-independent pde solution and derived quantities
	time-dependent pde solution and derived quantities
	pde eigenvalue solution and derived quantities

properties

	boundary condition for pde model
	coefficient assignments
	initial conditions over a region or region boundary
	initial conditions at mesh nodes
	algorithm options for solvers
	pde visualization of mesh and nodal results

topics

pde problem setup

workflow describing how to set up and solve pde problems using partial differential equation toolbox.
set dirichlet and neumann conditions for scalar pdes and systems of pdes. use functions when you cannot express your boundary conditions by constant input arguments.
specify the coefficient f in the equation.
set initial conditions for time-dependent problems or initial guess for nonlinear stationary problems.

solutions and their gradients

plot 2-d and 3-d pde solutions and their gradients using pdeplot and pdeplot3d.
plot 2-d pde solutions and their gradients using surf, mesh, quiver, and other matlab^® functions.
3-d solution and gradient plots with matlab functions
plot 3-d pde solutions, their gradients, and streamlines using surf, contourslice, quiver, and other matlab functions.
dimensions of stationary, time-dependent, and eigenvalue results at mesh nodes and arbitrary locations.

eigenvalue and wave problems

find the eigenvalues and eigenmodes of a square domain.
eigenvalues and eigenmodes of l-shaped membrane
use command-line functions to find the eigenvalues and the corresponding eigenmodes of an l-shaped membrane.
solve a standard second-order wave equation.
compute reflected waves from an object illuminated by incident waves.

workflows integrated with other toolboxes

solve a poisson's equation with dirichlet boundary conditions using pinn.
(medical imaging toolbox)
estimate bone stress and strain in a vertebra bone under axial compression using finite element (fe) analysis.

finite element method and partial differential equations

equations you can solve using pde toolbox
types of scalar pdes and systems of pdes that you can solve using partial differential equation toolbox.
transform pdes to the form required by partial differential equation toolbox.
description of the use of the finite element method to approximate a pde solution using a piecewise linear function.