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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
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Name |
Expression |
Type |
Semantics |
|---|---|---|---|
|
Calculate dx/dt := f(x,t) |
|
|
Calculates |
|
Calculate A := df/dx (x,t) |
|
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Calculates the Jacobian of f at x,t,
the result is stored into |