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).
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- val defaultStepSize: Double
The default step size for the t dimension
The default step size for the t dimension
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- val error: Double
Estimate of the error in calculating y
Estimate of the error in calculating y
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- def getError: Double
Get the error estimate.
Get the error estimate.
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- def integrate(f: Derivative, y0: Double, t: Double, t0: Double = 0.0, step: Double = defaultStepSize): Double
- f
the derivative function f(t, y)
- y0
the initial value of the y-function at time t0, y0 = y(t0)
- t
the time value at which to compute y(t)
- t0
the initial time
- step
the step size
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- Radau → Integrator
- def integrateV(f: Array[Derivative], y0: VectorD, t: Double, t0: Double = 0.0, step: Double = defaultStepSize): 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.
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).
- f
the array of derivative functions [f_j(t, y_j)]
- y0
the initial value vector, y0 = y(t0)
- t
the time value at which to compute y(t)
- t0
the initial time
- step
the step size
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- def integrateVV(f: Array[DerivativeV], y0: VectorD, t: Double, t0: Double = 0.0, step: Double = defaultStepSize): VectorD
- f
the array of derivative functions [f_j(t, y)]
- y0
the initial value vector, y0 = y(t0)
- t
the time value at which to compute y(t)
- t0
the initial time
- step
the step size
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- 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.
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.
- f
the array of functions whose Jacobian is sought
- y
the point (vector) at which to estimate the Jacobian
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- def solve(f: Array[DerivativeV], yn_1: VectorD, fn_1: VectorD, tn_1: Double, tn: Double, h: Double): Unit
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