Implicit System

Description

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.

Notation

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

Valid Expressions

Name	Expression	Type	Semantics
Calculate dx/dt := f(x,t)	`sys.first( x , dxdt , t )`	`void`	Calculates `f(x,t)`, the result is stored into dxdt
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`