Class Dopri

Basic Dormand–Prince integrator class for solving ordinary differential equations. For delay differential equations, see DDE.

Example

function lorenz(t: number, y: number[], dydt: number[]) {
    const y1 = y[0];
    const y2 = y[1];
    const y3 = y[2];
    dydt[0] = 10 * (y2 - y1);
    dydt[1] = 28 * y1 - y2 - y1 * y3;
    dydt[2] = -8 / 3 * y3 + y1 * y2;
};

const solver = new Dopri(lorenz, 3);
solver.initialise(0, [10, 1, 1]);
const solution = solver.run(10);
const t = [0, 1, 2, 3, 4, 5, 6, 7, 8, 10];
const y = solution(t);

Hierarchy

Implements

Constructors

constructor

Methods

initialise run statistics steps

Constructors

constructor

  • Parameters

    • rhs: RhsFn

      The right hand side function to be integrated

    • n: number

      The number of variables in the system to be integrated

    • control: Partial<DopriControlParam> = {}

      Optional control parameters to tune the integration

    • output: OutputFn = null

      Optional output function, to compute additional quantities related to the integration alongside the solution

    Returns Dopri

Methods

initialise

  • initialise(t: number, y: number[]): Dopri

  • Initialise the solver

    Parameters

    • t: number

      The time to start integrating from

    • y: number[]

      The initial conditions

    Returns Dopri

run

  • run(tEnd: number): ((t: number[]) => number[][])

  • Integrate the solution through to some time

    Parameters

    • tEnd: number

      End time of the integration

    Returns ((t: number[]) => number[][])

      • (t: number[]): number[][]

      • This is essentially a vectorised version of InterpolatedSolution, accepting a vector of times.

        Returns

        A vector of vectors; element [i][j] is the jth variable at the ith time in t

        Parameters

        • t: number[]

          Vector of times to request the solution at

        Returns number[][]

statistics

  • statistics(): { lastError: number; nEval: number; nSteps: number; nStepsAccepted: number; nStepsRejected: number; stiffNNonstiff: number; stiffNStiff: number }

  • Return statistics about the integration so far

    Returns { lastError: number; nEval: number; nSteps: number; nStepsAccepted: number; nStepsRejected: number; stiffNNonstiff: number; stiffNStiff: number }

    • lastError: number

      The last estimated error in the solution

    • nEval: number

      The number of evaluations of the rhs function

    • nSteps: number

      The number of steps attempted

    • nStepsAccepted: number

      The number of steps accepted

    • nStepsRejected: number

      The number of steps rejected

    • stiffNNonstiff: number

      The number of stiff checks that were non-stiff

    • stiffNStiff: number

      The number of stiff checks that were stiff

steps

  • steps(): number[]

  • Returns number[]

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