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integrate_const


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 -- Command: [T, Y] = integrate_const (@STEPPER,
     @FUN, TSPAN, X0, DT, OPTIONS)

     This function file can be called by an ODE solver function in order
     to integrate the set of ODEs on the interval [T0,T1] with a
     constant timestep DT.

     This function must be called with two output arguments: T and Y.
     Variable T is a column vector and contains the time stamps, instead
     Y is a matrix in which each column refers to a different unknown of
     the problem and the rows number is the same of T rows number so
     that each row of Y contains the values of all unknowns at the time
     value contained in the corresponding row in T.

     The first input argument must be a function_handle or an inline
     function representing the stepper, that is the function responsible
     for step-by-step integration.  This function discriminates one
     method from the others.

     The second input argument is the order of the stepper.  It is
     needed to compute the adaptive timesteps.

     The third input argument is a function_handle or an inline function
     that defines the set of ODE:

     y' = f(t,y).

     The third input argument is the time vector which defines
     integration interval, that is [TSPAN(1),TSPAN(END)] and all the
     intermediate elements are taken as times at which the solution is
     required.

     The fourth argument contains the initial conditions for the ODEs.

     The fifth input argument represents the fixed timestep and the last
     input argument contains some options that may be needed for the
     stepper.

See also: integrate_adaptive, integrate_n_steps.


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@FUN, TSPAN, X0, DT, OPTIONS)



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integrate_n_steps


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 -- Command: [T, Y] = integrate_n_steps
     (@STEPPER, @FUN, T0, X0, DT, N, OPTIONS)

     This function file can be called by an ODE solver function in order
     to integrate the set of ODEs on the interval [T0,T0 + N*DT] with a
     constant timestep dt and on a fixed number of steps.

     This function must be called with two output arguments: T and Y.
     Variable T is a column vector and contains the time stamps, instead
     Y is a matrix in which each column refers to a different unknown of
     the problem and the rows number is the same of T rows number so
     that each row of Y contains the values of all unknowns at the time
     value contained in the corresponding row in T.

     The first input argument must be a function_handle or an inline
     function representing the stepper, that is the function responsible
     for step-by-step integration.  This function discriminates one
     method from the others.

     The second input argument is the order of the stepper.  It is
     needed to compute the adaptive timesteps.

     The third input argument is a function_handle or an inline function
     that defines the set of ODE:

     y' = f(t,y).

     The third input argument is the starting point for the integration.

     The fourth argument contains the initial conditions for the ODEs.

     The fifth input argument represents the fixed timestep while the
     sixth contains the number of integration steps.

     The last argument is a struct with the options that may be needed
     by the stepper.

See also: integrate_adaptive, integrate_const.


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(@STEPPER, @FUN, T0, X0, DT, N, OPTIONS)





