matrixDE - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

Online Help

All Products    Maple    MapleSim


DEtools

  

matrixDE

  

find solutions of a linear system of ODEs in matrix form

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

matrixDE(A, B, t, method=matrixexp)

matrixDE(A, B, t, solution=solntype)

Parameters

A, B

-

coefficients of a system  ; if B not specified, then assumed to be a zero vector

t

-

independent variable of the system

method=matrixexp

-

(optional) matrix exponentials

solution=solntype

-

(optional) where solution=polynomial or solution=rational

Description

• 

The matrixDE command solves a system of linear ODEs of the form . If B is not specified then it is assumed to be the zero vector.

• 

An option of the form method = matrixexp can be specified to use matrix exponentials (in the case of constant coefficients).

• 

An option of the form solution = polynomial or solution = rational can be specified to search for polynomial or rational solution. In this case, the function invokes LinearFunctionalSystems[PolynomialSolution] or LinearFunctionalSystems[RationalSolution].

• 

The command returns a pair  with , which is an  by  matrix, and , which is an  by  vector. If you want the result expressed using Matrix instead, then use convert/Matrix on S(t).

  

A particular solution of the system can be then written in the form  where  is  by  and . If B is zero then P will also be zero.

• 

If a system is expressed in terms of equations, dsolve can be used instead.

Examples

Nonconstant homogeneous system

(1)

(2)

Matrix of arbitrary coefficients

Verification of solution

(3)

(4)

Nonhomogeneous system of two variables with constant coefficients

(5)

(6)

Verification of solution

(7)

(8)

Nonconstant homogeneous system with unknown coefficients

(9)

(10)

General nonhomogeneous system of two variables with constant coefficients

(11)

(12)

(13)

(14)

Finding a polynomial solution

(15)

(16)

See Also

DEtools

dsolve

LinearFunctionalSystems[PolynomialSolution]

LinearFunctionalSystems[RationalSolution]

 


Download Help Document