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rk4_solver(numer) Numerical Analysis rk4_solver(numer)

NAME

rk4_solver - Object that solves systems of differential equations using Runge_Kutta method.

DESCRIPTION

This object solves ordinary differential equation using Runge-Kutta method; independent parameter is time and its value is assumed to be the start value of the interval of the solution; dimension is the dimension of the system of equations; 1/resolution is the time interval for which solution is sought; number_of_steps is the number of steps in 1/resolution time period; the solution is generated by repeatedly calling rk4! method implemented in superclass; the state of the system is stored in function object after the solution is found. To find the system trajectory one has to repeatedly call tick! and store system state in data object.

SUPERCLASS

rk4_stepper

INSTANCE VARIABLES

time is the time of the initial state of the system.

resolution is the number of time points in the unit of time for which solution is sought.

number_of_steps is the number of steps of Runge_Kutta method for a single time interval size 1/resolution.

MESSAGES

number_of_steps=argument sets the value of number_of_steps.

number_of_steps? returns the value of number of steps.

resolution=argument sets the value of resolution.

resolution? returns the value of resolution.

time=argument sets the value of time.

time? returns the value of time.

tick! Computes the solution of the system for the time = time + 1 / resolution.

EXAMPLES

/* This code contains undefined object called system_function, therefore it cannot be executed directly; you should use your function instead that is defined object and responds to the messages state= and state? */

system_function new: my_function;

rk4_solver new: asolver function= my_function time = 1 resolution = 5 number_of_steps = 4 ;

asolver tick!;

data new: adata dimension=[asolver dimension?];

-- store the first data point

adata time = 1.2 value= [my_function state?];

asolver tick!

-- store the second data point

adata time = 1.4 value= [my_function state?];

-- ...