CAPD::DynSys Library  6.0.0
ODEs - nonrigorous methods

Table of Contents

Before reading this section be sure that you already familiar with sections Linear algebra and Defining functions and maps.

In this section we will give an overview on solving IVP for ODEs using the CAPD library.

Defined types and data structures

The main header file

#include "capd/capdlib.h"

defines the following types for computation in double (D) and long double (LD) precision.

  • DOdeSolver, LDOdeSolver - ODE solvers, they can integrate first order variational equations
  • DC2OdeSolver, LDC2OdeSolver - ODE solvers, they can integrate first and second order variational equations
  • DCnOdeSolver, LDCnOdeSolver - ODE solvers, they can integrate higher order variational equations
  • DTimeMap, LDTimeMap - integrate ODE over a time interval. They can integrate first order variational equations.
  • DC2TimeMap, LDC2TimeMap - integrate ODE over a time interval. They can integrate first and second order variational equations.
  • DCnTimeMap, LDCnTimeMap - integrate ODE over a time interval. They can integrate higher order variational equations.

Moreover, every class [Prefix]TimeMap defines public type SolutionCurve that is a functional object representing solution to IVP over time range. For example,

DTimeMap::SolutionCurve
LDTimeMap::SolutionCurve
DC2TimeMap::SolutionCurve
LDC2TimeMap::SolutionCurve
DCnTimeMap::SolutionCurve
LDCnTimeMap::SolutionCurve
capd::diffAlgebra::SolutionCurve
Definition: SolutionCurve.h:131

In the CAPD we offer for you three strategies of solving IVP for ODEs. You can choose from

  • one-step numerical scheme based on high-order Taylor method
  • a method for computation of the solution after a given time. This approach combines one-step scheme with automatic step control.
  • a method for computation of a solution curve (as a functional object) over a time range.

More detailed explanation is given in the following sections.