方程求解
您可以求解代数方程、微分方程和微分代数方程 (DAE)。
求解代数方程以获得精确的解析解或高精度的数值解。对于解析解，请使用 solve；对于数值解，请使用 vpasolve。对于求解线性方程，请使用 linsolve。这些求解器函数可以灵活地处理复杂的问题。请参阅Choose an Approach for Solving Equations Using solve Function。
使用 dsolve 求解微分方程。使用符号函数创建这些微分方程。请参阅创建符号函数。
通过以下方式求解微分代数方程 (DAE)：先使用 Symbolic Math Toolbox™ 函数将这些方程的微分指数减少到 1 或 0，然后使用 ode15i、ode15s 或 ode23t 等 MATLAB® 求解器。请参阅Solve Differential Algebraic Equations (DAEs)。
实时编辑器任务
| 求解符号方程 | Find analytic solutions of symbolic equations in Live Editor |
函数
主题
- Solve Algebraic Equations
Solve equations analytically, return full solutions, and visualize results.
- 求解微分方程
在具有或不具有初始条件的情况下使用
dsolve函数以解析方式求解微分方程。 - Solve Differential Algebraic Equations (DAEs)
This example show how to solve differential algebraic equations (DAEs) by using MATLAB® and Symbolic Math Toolbox™.
精选示例
The Physics of the Damped Harmonic Oscillator
Explores the physics of the damped harmonic oscillator by solving the equations of motion in the case of no driving forces. This example investigates the cases of under-, over-, and critical-damping.
Validate Simulink Model Using Symbolic Math Toolbox
Model a bouncing ball, which is a classical hybrid dynamic system. This model includes both continuous dynamics and discrete transitions. It uses the Symbolic Math Toolbox™ to help explain some of the theory behind ODE solving in the 弹球的仿真 (Simulink).
Derive and Apply Inverse Kinematics to Two-Link Robot Arm
Derive and apply inverse kinematics to a two-link robot arm by using MATLAB and Symbolic Math Toolbox.
Gauss-Laguerre Quadrature Evaluation Points and Weights
Solve polynomial equations and systems of equations, and work with the results using Symbolic Math Toolbox™.
Simulate a Stochastic Process Using the Feynman–Kac Formula
Obtains the partial differential equation that describes the expected final price of an asset whose price is a stochastic process given by a stochastic differential equation.
The Black–Scholes Formula for Call Option Price
Calculate the call option price using the Black–Scholes formula. This example uses vpasolve to numerically solve the problems of finding the spot price and implied volatility from the Black–Scholes formula.
Heating of Finite Slab
Find the temperature distribution of a one-dimensional finite slab by solving the differential equation using the method of separation of variables.
Derive Equations of Motion and Simulate Cart-Pole System
Derive the equations of motion for the cart-pole system using Symbolic Math Toolbox™ and then simulate the cart-pole system using the ode45 solver. In the later sections of the example, you explore how to derive the equations in other forms that can be used to numerically simulate the system (and validate the results) using different tools, such as Simulink®, Simscape™ Multibody™, and Robotics System Toolbox™.
Finite Element Formulation for Timoshenko Beam Problem
Apply the finite element method (FEM) to solve a Timoshenko beam problem, using both linear and quadratic basis functions for analysis. The Timoshenko beam theory is a 1-D problem that reduces the complex 3-D problem of beam deformation to a set of 1-D differential equations along the length of the beam. In contrast to the Euler–Bernoulli beam theory, which does not consider shear deformation, the Timoshenko beam theory accounts for both shear deformation and rotational bending effects. The Timoshenko beam theory is generally more accurate for short, thick beams where shear deformation cannot be neglected. Using a cantilever beam and a beam fixed at both ends, this example discusses the analytical solutions of the Timoshenko beam problem and compares them with the FEM solutions.
