DEtools[matrix_riccati] - solve a Matrix Riccati differential equation
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Calling Sequence
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matrix_riccati(A, K, Z0, t)
matrix_riccati(A, K, Z0, t=t0)
matrix_riccati(A, K, t)
matrix_riccati(A, K, t=t0)
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Parameters
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A, K
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Matrix coefficients of the Riccati Matrix Equation
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Z0
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Matrix representing the initial conditions for t=t0
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t
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independent variable
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t0
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position of initial conditions
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Description
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The Matrix Riccati differential equation is
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The command with(DEtools,matrix_riccati) allows the use of the abbreviated form of this command.
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Examples
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>
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The unknowns are
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A simple example would be
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The matrix with the initial values and is
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The system of equations represented by these matrices is thus
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The two coupled odes are
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The matrix solution to this matrix system of equations with initial conditions at is computed as:
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Recalling the form of , the solution to the system of odes is constructed from as
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This result can be verified with odetest
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