Ecuaciones diferenciales ordinarias

Mecanismos de solución de problemas de valores iniciales de ecuaciones diferenciales ordinarias

Los mecanismos de solución de ecuaciones diferenciales ordinarias (ODE) en MATLAB^® resuelven problemas de valores iniciales con una gran variedad de propiedades. Los mecanismos de solución pueden funcionar en problemas rígidos y no rígidos, problemas con una matriz de masa, ecuaciones algebraicas diferenciales (DAE) o problemas completamente implícitos. Para obtener más información, consulte Elegir un solver de ODE.

Solucione problemas y establezca opciones con una interfaz visual con la tarea Solve ODE de Live Editor.

Objetos

`ode`	Ordinary differential equations (Desde R2023b)
`odeMassMatrix`	ODE mass matrix (Desde R2023b)
`odeJacobian`	ODE Jacobian matrix (Desde R2023b)
`odeEvent`	ODE event definition (Desde R2023b)
`odeSensitivity`	ODE sensitivity analysis (Desde R2024a)
`odeDelay`	ODE delay definition (Desde R2025a)
`ODEResults`	Results of ODE integration (Desde R2023b)

Tareas de Live Editor

Solve ODE

Solve system of ordinary differential equations in the Live Editor (Desde R2024b)

Funciones

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Mecanismos de solución no rígidos

`ode45`	Resolver ecuaciones diferenciales no rígidas; método de orden intermedio
`ode23`	Resolver ecuaciones diferenciales no rígidas; método de orden bajo
`ode78`	Solve nonstiff differential equations — high order method (Desde R2021b)
`ode89`	Solve nonstiff differential equations — high order method (Desde R2021b)
`ode113`	Solve nonstiff differential equations — variable order method

Mecanismos de solución rígidos

`ode15s`	Resolver ecuaciones diferenciales y DAE rígidas; método de orden variable
`ode23s`	Solve stiff differential equations — low order method
`ode23t`	Solve moderately stiff ODEs and DAEs — trapezoidal rule
`ode23tb`	Solve stiff differential equations — trapezoidal rule + backward differentiation formula

Mecanismos de solución completamente implícitos

`ode15i`	Solve fully implicit differential equations — variable order method
`decic`	Compute consistent initial conditions for `ode15i`

Opciones get/set

`odeget`	Extract ODE option values
`odeset`	Create or modify options structure for ODE and PDE solvers

Evaluar y ampliar la solución

`deval`	Evaluate differential equation solution structure
`odextend`	Extend solution to ODE

Temas

Resolver ODE

Elegir un solver de ODE
Información contextual sobre ODE, descripciones de solver, algoritmos y resumen de ejemplos.
Resumen de opciones de ODE
Uso de odeset y tabla que indica qué opciones funcionan con cada solver de ODE.
Ubicación de eventos de EDO
Detecte eventos durante la solución de EDO.
Resolver ecuaciones diferenciales ordinarias (ODE) no rígidas
Esta página contiene dos ejemplos de resolución de ecuaciones diferenciales ordinarias no rígidas con ode45.
Solve Stiff ODEs
This page contains two examples of solving stiff ordinary differential equations using ode15s.
Solve Differential Algebraic Equations (DAEs)
Solve ODEs with a singular mass matrix.
Nonnegative ODE Solution
This topic shows how to constrain the solution of an ODE to be nonnegative.
Troubleshoot Common ODE Problems
FAQ containing common problems and solutions.

Diferenciación automática en las ODE

Resolve Error: Unable to Assign Expression During Automatic Differentiation
Troubleshoot expression initialization for automatic differentiation.
Supported Operations on Expressions
List of supported operations on expressions for automatic differentiation.
Automatic Differentiation Background
Learn the theoretical aspects of automatic differentiation and its forward and reverse modes.

Ejemplos destacados

Resolver ecuaciones presa-depredador

En este ejemplo se muestra cómo resolver una ecuación diferencial en la que se representa un modelo presa-depredador utilizando métodos de integración Runge-Kutta de tamaño de paso variable. El método ode23 utiliza un par de fórmulas de segundo y tercer orden para obtener una precisión intermedia y el método ode45 utiliza un par de cuarto y quinto orden para obtener una mayor precisión.

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Solve Equations of Motion for Baton Thrown into Air

Solves a system of ordinary differential equations that model the dynamics of a baton thrown into the air [1]. The baton is modeled as two particles with masses $m_{1}$ and $m_{2}$ connected by a rod of length $L$ . The baton is thrown into the air and subsequently moves in the vertical xy-plane subject to the force due to gravity. The rod forms an angle $θ$ with the horizontal and the coordinates of the first mass are $(x, y)$ . With this formulation, the coordinates of the second mass are $(x + L \cos θ, y + L \sin θ)$ .

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Sensitivity Analysis of Epidemic ODE Parameters

Perform sensitivity analysis on the parameters of an ordinary differential equation (ODE) system that models the spread of a disease in an epidemic.

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Solve Celestial Mechanics Problem with High-Order Solvers

Use ode78 and ode89 to solve a celestial mechanics problem that requires high accuracy in each step from the ODE solver for a successful integration. Both ode45 and ode113 are unable to solve the problem using the default error tolerances. Even with more stringent error thresholds, ode89 performs best on the problem due to the high accuracy of the Runge-Kutta formulas it uses in each step.

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Solve Stiff Transistor Differential Algebraic Equation

Solve a stiff differential algebraic equation (DAE) that describes an electrical circuit [1]. The one-transistor amplifier problem coded in the example file amp1dae.m can be rewritten in semi-explicit form, but this example solves it in its original form $M u^{'} = ϕ (u)$ . The problem includes a constant, singular mass matrix $M$ .

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Solve System of ODEs with Multiple Initial Conditions

Compares two techniques to solve a system of ordinary differential equations with multiple sets of initial conditions.

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Solve ODE with Strongly State-Dependent Mass Matrix

Solve Burgers' equation using a moving mesh technique [1]. The problem includes a mass matrix, and options are specified to account for the strong state dependence and sparsity of the mass matrix, making the solution process more efficient.

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