Pure quadrature
Integration of quadrature equations
Syntax
... = cvode( ... , quadRhs = fun, options) ... = ida( ... , quadRhs = fun, options)
Arguments
| fun | A Scilab function, a list, a string. |
| options | a sequence of optional named arguments (see the solvers options) and below for quadrature specific options. |
| t | vector of time points used by the solver. |
| y | array of solution at time values in t |
| info | MList of |
| sol | MList of |
Description
During integration, the solver can compute simultaneously quadratures/integrals of a function g depending on time t and solution when solving an ODE or a DAE:
These quantities could be added as new states and trivial equations in the original problem since 
but giving them separately avoids computing useless Jacobians and saves the solver effort.
The value of g is given by the output of fun, which has the same prototype as a classical ODE rhs or DAE residual. After the solver call
the quadrature variables are retrieved in the "q" field of either the info or sol output argument,
as in the following examples (typically, only the final value of q will be of interest). The initial values of the quadrature variables are zero
by default but can be set with the option yQ0. Note
Examples
function dyqdt=g(t, y) dyqdt = t*y(1); end [t,y,info] = cvode(%SUN_vdp1, [0 1], [1 2], quadRhs=g); info.q
function dyqdt=g(t, y, yp) dyqdt = y(2); end y0 = [1-1e-6; 1e-6; 0]; yp0 = [-2e-7; 1.5e-7; 5e-8]; [t,y,info] = ida(%SUN_sir, [0,200], y0, yp0, quadRhs=g); info.q
Options
| yQ0 | a double array giving the initial state of the quadrature variable. |
| quadErrCon | By default, QuadErrCon is set to %f. If quadErrCon=%t then quadrature variables are included in the error tests. |
| rtolQ | The scalar relative tolerance to control the local error estimator when quadErrCon=%t (default value is 1e-4). |
| atolQ | The absolute tolerance controlling the local error when quadErrCon=%t. It can be a scalar or an array of the same dimension as the quadrature variable (default value is 1e-6). |
See also
- arkode — SUNDIALS ordinary differential equation additive Runge-Kutta solver
- cvode — SUNDIALS ordinary differential equation solver
- ida — SUNDIALS differential-algebraic equation solver
- User functions — Coding user functions used by SUNDIALS solvers
- Options (ODE and DAE solvers) — Changing the default behavior of solver
- SUN_Clink — Compiling and linking a C user function
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