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This concept describes how to define a ODE that can be solved by an implicit routine. Implicit routines need not only the function f(x,t) but also the Jacobian df/dx = A(x,t). A is a matrix and implicit routines need to solve the linear problem Ax = b. In odeint this is implemented with use of Boost.uBLAS, therefore, the state_type implicit routines is ublas::vector and the matrix is defined as ublas::matrix.
System
A type that is a model of Implicit
System
Time
A type representing the time of the ODE
sys
An object of type System
x
Object of type ublas::vector
dxdt
Object of type ublas::vector
jacobi
Object of type ublas::matrix
t
Object of type Time
Name 
Expression 
Type 
Semantics 

Calculate dx/dt := f(x,t) 


Calculates 
Calculate A := df/dx (x,t) 


Calculates the Jacobian of f at x,t,
the result is stored into 