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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


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