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reduceDifferentialOrder

Reduce system of higher-order differential equations to equivalent system of first-order differential equations

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Syntax

[neweqs，newvars] =降低差异（eqs，vars）
[newEqs,newVars,R] = reduceDifferentialOrder(eqs,vars)

Description

example

[newEqs,newVars] =降低差异（eqs,vars)rewrites a system of higher-order differential equationseqs作为一阶微分方程的系统newEqs通过代替衍生物eqswith new variables. Here,newVarsconsists of the original variablesvarsaugmented with these new variables.

example

[newEqs,newVars,R] =降低差异（eqs,vars)returns the matrixRthat expresses the new variables innewVars作为原始变量的衍生物vars.

Examples

Reduce Differential Order of DAE System

Reduce a system containing higher-order DAEs to a system containing only first-order DAEs.

Create the system of differential equations, which includes a second-order expression. Here,x(t)和y（t）are the state variables of the system, andc1和c2是参数。将方程式和变量指定为两个符号向量：方程为符号方程的向量，而变量是符号函数调用的向量。

syms x(t) y(t) c1 c2 eqs = [diff(x(t), t, t) + sin(x(t)) + y(t) == c1*cos(t),... diff(y(t), t) == c2*x(t)]; vars = [x(t), y(t)];

Rewrite this system so that all equations become first-order differential equations. ThereduceDifferentialOrderfunction replaces the higher-order DAE by first-order expressions by introducing the new variableDxt(t). It also represents all equations as symbolic expressions.

[newEqs, newVars] = reduceDifferentialOrder(eqs, vars)
neweqs = diff（dxt（t），t） + sin（x（t）） + y（t）-c1*cos（t）diff（y（t），t）-c2*x（t）dxt（t）） -  diff（x（t），t）newvars = x（t）y（t）dxt（t）

Show Relations Between Generated and Original Variables

Reduce a system containing a second- and a third-order expression to a system containing only first-order DAEs. In addition, return a matrix that expresses the variables generated byreduceDifferentialOrder通过该系统的原始变量。

创建一个微分方程系统，其中包括二阶和三阶表达式。这里，x(t)和y（t）are the state variables of the system. Specify the equations and variables as two symbolic vectors: equations as a vector of symbolic equations, and variables as a vector of symbolic function calls.

syms x（t）y（t）f（t）eqs = [diff（x（t），t，t）== diff（f（t），t，t，t，t），diff（y（t），，y（t），，t，t，t）== diff（f（t），t，t）];vars = [x（t），y（t）];

CallreduceDifferentialOrderwith three output arguments. This syntax returns matrixRwith two columns: the first column contains the new variables, and the second column expresses the new variables as derivatives of the original variables,x(t)和y（t）.

[neweqs，newvars，r] =降低iFferentiFentialOrder（eqs，vars）
neweqs = diff（dxt（t），t） -  diff（f（t），t，t，t，t）diff（dytt（t），t） -  diff（f（t），t，t，t）dxt（t）-diff（x（t），t）dyt（t） -  diff（y（t），t）dytt（t） -  diff（dyt（t），t）newvars = x（t）y（t）y（t）dxt（t）dyt（t）dytt（t）r = [dxt（t），diff（x（t），t）] [dyt（t），diff（y（t），t），t）]diff（y（t），t，t）]

Input Arguments

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包含高阶微分方程的系统, specified as a vector of symbolic equations or expressions.

原始微分方程的变量, specified as a vector of symbolic functions, or function calls, such asx(t).

例子：[x（t），y（t）]

Output Arguments

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System of first-order differential equations, returned as a column vector of symbolic expressions.

Extended set of variables, returned as a column vector of symbolic function calls. This vector includes the original state variablesvarsfollowed by the generated variables that replace the higher-order derivatives ineqs.

Relations between new and original variables, returned as a symbolic matrix with two columns. The first column contains the new variablesnewVars. The second column contains their definition as derivatives of the original variablesvars.

版本历史

在R2014b中引入

See Also

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