dev.nm.analysis.differentialequation.ode.ivp.problem

Class ODE1stOrder

java.lang.Object

dev.nm.analysis.differentialequation.ode.ivp.problem.ODE1stOrder

Direct Known Subclasses:

ODE1stOrderWith2ndDerivative

public class ODE1stOrder
extends Object

A first order ordinary differential equation (ODE) initial value problem (IVP) takes the following form. \[ y' = f(x, y) \\ y(x_0) = y_0 \] where \(y_{0}\) is known, and the solution of the problem is y(x) for the integrating interval \([x_{0}, x_{1}]\).

Supplying a system

For a DerivativeFunction, evaluate(t, y) must return the vector of derivatives in the same component order as the initial state. Its dimension must match y0.size(). Components of y use one-based indexing. Return a fresh derivative vector rather than modifying the supplied state. The initial state is copied by this constructor.

See Also:

EulerMethod, Wikipedia: Ordinary differential equation

Constructor Summary

Constructors

Constructor and Description
ODE1stOrder(DerivativeFunction dy, Vector y0, double x0, double x1) Constructs a first order ODE with the given vector-valued function and its initial values.
ODE1stOrder(ODE ode) Reduces a high order ODE to a system of first order ODEs.
ODE1stOrder(RealScalarFunction[] Y, double[] y0, double x0, double x1) Constructs a system of first order ODEs \(\{Y_{i}\}\) with their initial values \(\{y_{i0}\}\). \[ y_1' = Y_1(x, y_1, y_2, y_3, ...), y_1(0) = y_{10}\\ y_2' = Y_2(x, y_1, y_2, y_3, ...), y_2(0) = y_{20}\\ y_3' = Y_3(x, y_1, y_2, y_3, ...), y_3(0) = y_{30}\\
ODE1stOrder(RealVectorFunction F, Vector y0, double x0, double x1) Constructs a first order ODE with the given vector-valued function and its initial values.

Method Summary

Modifier and Type	Method and Description
static DerivativeFunction	convertToDerivativeFunction(RealVectorFunction F, int dimension) Converts the given vector function to a first order derivative function.
int	dimension() Gets the dimension of y.
DerivativeFunction	dy() Gets the first order derivative function.
double	x0() Gets the start point of the integrating interval \([x_{0}, x_{1}]\).
double	x1() Gets the end point of the integrating interval \([x_{0}, x_{1}]\).
Vector	y0() Gets the initial value of y, that is, \(y_{0}\).

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

ODE1stOrder

public ODE1stOrder(DerivativeFunction dy,
                   Vector y0,
                   double x0,
                   double x1)

Constructs a first order ODE with the given vector-valued function and its initial values.

Parameters:

dy - the first order derivative function y' = F(x, y)

y0 - \(y_{0}\)

x0 - the start point of the integrating interval \([x_{0}, x_{1}]\)

x1 - the end point of the integrating interval \([x_{0}, x_{1}]\)

ODE1stOrder

public ODE1stOrder(RealScalarFunction[] Y,
                   double[] y0,
                   double x0,
                   double x1)

Constructs a system of first order ODEs \(\{Y_{i}\}\) with their initial values \(\{y_{i0}\}\). \[ y_1' = Y_1(x, y_1, y_2, y_3, ...), y_1(0) = y_{10}\\ y_2' = Y_2(x, y_1, y_2, y_3, ...), y_2(0) = y_{20}\\ y_3' = Y_3(x, y_1, y_2, y_3, ...), y_3(0) = y_{30}\\ ... \]

Parameters:

Y - the differentials, \(\{Y_{i}\}\)

y0 - the initial values, \(\{y_{i}(0)\}\)

x0 - the start point of the integrating interval \([x_{0}, x_{1}]\)

x1 - the end point of the integrating interval \([x_{0}, x_{1}]\)

ODE1stOrder

public ODE1stOrder(RealVectorFunction F,
                   Vector y0,
                   double x0,
                   double x1)

Constructs a first order ODE with the given vector-valued function and its initial values.

Parameters:

F - F(x, y) = y'

y0 - \(y_{0}\)

x0 - the start point of the integrating interval \([x_{0}, x_{1}]\)

x1 - the end point of the integrating interval \([x_{0}, x_{1}]\)

ODE1stOrder

public ODE1stOrder(ODE ode)

Reduces a high order ODE to a system of first order ODEs.

Parameters:

ode - the high order ODE

See Also:

Wikipedia: Reduction to a first order system

Method Detail

convertToDerivativeFunction

public static DerivativeFunction convertToDerivativeFunction(RealVectorFunction F,
                                                             int dimension)

Converts the given vector function to a first order derivative function.

Parameters:

F - the vector-valued function \(F(x, y_{1}, \ldots , y_{n})\)

dimension - the dimension of the derivative function

Returns:

the converted first order derivative function

dy

public DerivativeFunction dy()

Gets the first order derivative function.

Returns:

the first order derivative function

dimension

public int dimension()

Gets the dimension of y.

Returns:

the dimension of y

y0

public Vector y0()

Gets the initial value of y, that is, \(y_{0}\).

Returns:

\(y_{0}\)

x0

public double x0()

Gets the start point of the integrating interval \([x_{0}, x_{1}]\).

Returns:

\(x_{0}\)

x1

public double x1()

Gets the end point of the integrating interval \([x_{0}, x_{1}]\).

Returns:

\(x_{1}\)