y, with respect to a single independent variable,t, usually referred to as time. The notation used here for representing derivatives ofywith respect totisy′for a first derivative,y′′for a second derivative, and so on. Theorderof the ODE is equal to the highest-order derivative of...
The van der Pol equation is a second order ODE y′′1−μ(1−y21)y′1+y1=0. Solve the van der Pol equation withμ=1usingode45. The functionvdp1.mships with MATLAB® and encodes the equations. Specify a single output to return a structure containing information about the solution,...
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The van der Pol equation is a second order ODE y′′1−μ(1−y21)y′1+y1=0. Solve the van der Pol equation with μ=1000 using ode15s. The function vdp1000.m ships with MATLAB® and encodes the equations. Specify a single output to return a structure containing information about...
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1、ode23s介绍 ode23s(stiff differential equation solver)是MATLAB中的一种求解刚性(stiff)微分方程的数值方法。刚性微分方程通常具有多个时间尺度差异较大的变量,并且其中至少有一个变量具有快速变化的特性。 ode23s方法使用了一个隐式的一步法(implicit one-step method),结合了 Rosenbrock 方法和 backward differenti...
Consider the second order initial value problem x = f (t, x, x ), t ∈ [a, b] x(a) = xa x (a) = xpa If we set y = x , then the sxstem can be written as d dt x y = y f (t, x, y) x(a) = xa y(a) = xpa The numerical approximation can now be carrried...
Consider the second-order ODE y′′+2xy′+1x4y=0. The equation is defined on the interval[13π,1]subject to the boundary conditions y(13π)=0, y(1)=sin(1). To solve this equation in MATLAB®, you need to write a function that represents the equation as a system of first-order...
ode15iis a variable-step, variable-order (VSVO) solver based on the backward differentiation formulas (BDFs) of orders 1 to 5.ode15iis designed to be used with fully implicit differential equations and index-1 differential algebraic equations (DAEs). The helper functiondeciccomputes consistent...
The values indicate which event the solver detected.Algorithms ode23tb is an implementation of TR-BDF2, an implicit Runge-Kutta formula with a trapezoidal rule step as its first stage and a backward differentiation formula of order two as its second stage. By construction, the same iteration ...