Mathematics > Numerical Integration and Differential Equations

44 functions in MATLAB › Mathematics > Numerical Integration and Differential Equations.

Boundary Value Problems

`bvp4c`	Solves boundary value problems for ordinary differential equations.
`bvp5c`	Solves boundary value problems with a fourth-order method that controls the true error.
`bvpget`	Reads a named option from a boundary value problem options structure.
`bvpinit`	Builds the initial mesh and guess for a boundary value problem solver.
`bvpset`	Creates or updates the options structure used by the boundary value problem solvers.
`bvpxtend`	Extends a boundary value problem solution to a new interval end.

Numerical Integration and Differentiation

`cumtrapz`	Cumulative integral by the trapezoidal rule.
`dblquad`	Numerical double integral over a rectangle (older interface).
`del2`	Discrete Laplacian of an array.
`gradient`	Numerical gradient (finite-difference derivative) of sampled data.
`integral`	Numerical integral of a function of one variable.
`integral2`	Numerical double integral over a rectangle or a region with variable limits.
`integral3`	Numerical triple integral over a box or a region with variable limits.
`quad`	Numerical integral by adaptive Simpson quadrature (older interface).
`quad2d`	Numerical double integral using tiled adaptive Gauss-Kronrod quadrature.
`quadgk`	Adaptive Gauss-Kronrod quadrature, including infinite limits and singular endpoints.
`quadl`	Numerical integral by adaptive Lobatto quadrature (older interface).
`quadv`	Adaptive Simpson quadrature of a vector-valued function of one variable.
`trapz`	Numerical integral of sampled data by the trapezoidal rule.
`triplequad`	Numerical triple integral over a box (older interface).

Delay Differential Equations

`dde23`	Solves delay differential equations with constant delays.
`ddeget`	Reads a named option from a delay differential equation options structure.
`ddensd`	Solves neutral delay differential equations with state-dependent delays.
`ddesd`	Solves delay differential equations with time- or state-dependent delays.
`ddeset`	Creates or updates the options structure used by the delay equation solvers.

Ordinary Differential Equations

`decic`	Finds consistent initial conditions for a fully implicit differential equation.
`deval`	Evaluates a differential equation solution structure at given points.
`ode113`	Variable-order Adams-Bashforth-Moulton solver for nonstiff differential equations.
`ode15i`	Variable-order solver for fully implicit differential equations f(t, y, y') = 0.
`ode15s`	Variable-order solver for stiff differential equations and index-1 algebraic systems.
`ode23`	Low-order Runge-Kutta solver for nonstiff differential equations.
`ode23s`	One-step solver for stiff differential equations, based on a modified Rosenbrock formula.
`ode23t`	Trapezoidal-rule solver for moderately stiff equations and differential-algebraic systems.
`ode23tb`	TR-BDF2 solver for stiff differential equations at crude tolerances.
`ode45`	Default Runge-Kutta solver for nonstiff ordinary differential equations.
`ode78`	Seventh- and eighth-order Runge-Kutta solver for nonstiff equations with tight tolerances.
`ode89`	Eighth- and ninth-order Runge-Kutta solver for nonstiff equations with very tight tolerances.
`odeget`	Reads a named option from an ODE options structure.
`odeset`	Creates or updates the options structure used by the ODE solvers.
`odextend`	Extends the solution of an ODE initial value problem to a later time.
`solutionFcn`	Method of the ode object: returns a function handle that evaluates the solution at any time.
`solve`	Method of the ode object: integrates the differential equation it defines.

1-D Partial Differential Equations

`pdepe`	Solves one-dimensional parabolic and elliptic partial differential equations.
`pdeval`	Evaluates a pdepe solution and its derivative at chosen points.