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ode_root

ordinary differential equation solver with roots finding

Syntax

[y, rd, w, iw] = ode("root", y0, t0, t [,rtol [,atol]], f [,jac], ng, g [,w,iw])

Arguments

y0

a real vector or matrix (initial conditions).

t0

a real scalar (initial time).

t

a real vector (times at which the solution is computed).

f

an external function (Scilab function, list or string), computes the value of f(t, y). It is the right hand side of the differential equation. See ode help for more details.

rtol, atol

a real constants or real vectors of the same size as y.

jac

an external function (a Scilab fuction, list or string), computes the Jacobian of the function f(t, y). See ode help for more details.

ng

an integer, number of components of g function

g

an external function (a Scilab fuction, list or string) with the syntax g(t, y), returns a vector of size ng. Each component defines a surface.

y

a real vector or matrix. The solution.

rd

a real vector.

w, iw

vectors of real numbers. See ode() optional output

Description

With this syntax (first argument equal to "root") ode computes the solution of the differential equation dy/dt=f(t,y) until the state y(t) crosses the surface g(t,y)=0.

g should give the equation of the surface. It is an external i.e. a function with specified syntax, or the name of a Fortran subroutine or a C function (character string) with specified syntax or a list:

a Scilab function

Its syntax must be

r = g(t,y)

this function must return a vector with ng elements.

a list

This form of external is used to pass parameters to the function. It must be as follows:

list(g, p1, p2,...)

where the syntax of the function g is now

r = g(t, y, p1, p2,...)

a character string

it must refer to the name of a C or Fortran routine. Assuming that <g_name> is the given name,

  • The Fortran calling sequence must be

    subroutine <g_name>(n, t, y, ng, gout)
double precision t, y(*), gout(*)
integer n, ng

  • The C syntax must be

    void <g_name>(int *n, double *t, double *y, int *ng, double *gout)

where

  • t is a real scalar (time)

  • y is a real vector (the state)

  • ng is the number of constraints

  • n the dimension of the state

  • gout is the results array.

See the ode_root help for more details.

Output rd is a 1 x k vector. The first entry contains the stopping time. Other entries indicate which components of g have changed sign. k larger than 2 indicates that more than one surface ((k-1) surfaces) have been simultaneously traversed.

Other arguments and other options are the same as for ode, see the ode help.

Examples

// Integration of the differential equation
// dy/dt=y , y(0)=1, and finds the minimum time t such that y(t)=2
deff("ydot = f(t,y)", "ydot=y")
deff("z = g(t,y)", "z=y-2")
y0 = 1; ng = 1;
[y,rd] = ode("root", y0, 0, 2, f, ng, g)

g = #(t, y) -> (y - [2;2;33]);
[y,rd] = ode("root", 1, 0, 2, f, 3, g)

See also


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