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43 lines
1.6 KiB
Plaintext
43 lines
1.6 KiB
Plaintext
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[/============================================================================
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Boost.odeint
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Copyright 2011 Mario Mulansky
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Copyright 2011-2012 Karsten Ahnert
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Use, modification and distribution is subject to the Boost Software License,
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Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
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http://www.boost.org/LICENSE_1_0.txt)
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=============================================================================/]
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[section Implicit System]
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[heading Description]
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This concept describes how to define a ODE that can be solved by an implicit routine.
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Implicit routines need not only the function /f(x,t)/ but also the Jacobian /df/dx = A(x,t)/.
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/A/ is a matrix and implicit routines need to solve the linear problem /Ax = b/.
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In odeint this is implemented with use of __ublas, therefore, the ['state_type] implicit routines is ['ublas::vector] and the matrix is defined as ['ublas::matrix].
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[heading Notation]
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[variablelist
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[[`System`] [A type that is a model of `Implicit System`]]
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[[`Time`] [A type representing the time of the ODE]]
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[[`sys`] [An object of type `System`]]
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[[`x`] [Object of type ublas::vector]]
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[[`dxdt`] [Object of type ublas::vector]]
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[[`jacobi`] [Object of type ublas::matrix]]
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[[`t`] [Object of type `Time`]]
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]
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[heading Valid Expressions]
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[table
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[[Name] [Expression] [Type] [Semantics]]
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[[Calculate ['dx/dt := f(x,t)]] [`sys.first( x , dxdt , t )`] [`void`] [Calculates `f(x,t)`, the result is stored into dxdt] ]
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[[Calculate ['A := df/dx (x,t)]] [`sys.second( x , jacobi , t )`] [`void`] [Calculates the Jacobian of /f/ at /x/,/t/, the result is stored into `jacobi`] ]
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]
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[endsect]
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