Radau

scalation.dynamics.Radau
object Radau extends Integrator

The Radau object implements Radau IIA, which is a simple Ordinary Differential Equation ODE solver for moderately stiff systems. Solve for y given

d/dt  y = f(t, y).

Attributes

Graph
Supertypes
trait Integrator
class Object
trait Matchable
class Any
Self type
Radau.type

Members list

Value members

Concrete methods

def integrate(f: Derivative, y0: Double, t: Double, t0: Double, step: Double): Double

Attributes

def integrateVV(f: Array[DerivativeV], y0: VectorD, t: Double, t0: Double, step: Double): VectorD

Attributes

def jacobian(f: Array[DerivativeV], y: VectorD, t: Double): MatrixD

Compute the Jacobian matrix for a vector-valued derivative function represented as an array of scalar-valued functions. The i-th row in the matrix is the gradient of the i-th function.

Compute the Jacobian matrix for a vector-valued derivative function represented as an array of scalar-valued functions. The i-th row in the matrix is the gradient of the i-th function.

Value parameters

f

the array of functions whose Jacobian is sought

y

the point (vector) at which to estimate the Jacobian

Attributes

def solve(f: Array[DerivativeV], yn_1: VectorD, fn_1: VectorD, tn_1: Double, tn: Double, h: Double): Unit

Attributes

Inherited methods

def getError: Double

Get the error estimate.

Get the error estimate.

Attributes

Inherited from:
Integrator
def integrateV(f: Array[Derivative], y0: VectorD, t: Double, t0: Double, step: Double): VectorD

Apply the integrate method to each derivative to compute the trajectory of a time-dependent vector function y(t) governed by a separable system of Ordinary Differential Equations (ODE's) where [f_j(t, y_j)] is an array of derivative functions. Each derivative function takes a scalar t and a scalar y_j = y(j).

Apply the integrate method to each derivative to compute the trajectory of a time-dependent vector function y(t) governed by a separable system of Ordinary Differential Equations (ODE's) where [f_j(t, y_j)] is an array of derivative functions. Each derivative function takes a scalar t and a scalar y_j = y(j).

Value parameters

f

the array of derivative functions [f_j(t, y_j)]

step

the step size

t

the time value at which to compute y(t)

t0

the initial time

y0

the initial value vector, y0 = y(t0)

Attributes

Inherited from:
Integrator

Inherited fields

protected val defaultStepSize: Double

The default step size for the t dimension

The default step size for the t dimension

Attributes

Inherited from:
Integrator
protected var error: Double

Estimate of the error in calculating y

Estimate of the error in calculating y

Attributes

Inherited from:
Integrator