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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
            
TimeA type representing the time of the ODE
sys
              An object of type System
            
xObject of type ublas::vector
dxdtObject of type ublas::vector
jacobiObject 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  |