Solve ordinary differential equations (ODEs) numerically with Typescript

Reference URL

I modified the Typescript codes in https://zenn.dev/yonda/articles/71aef28aa46fcb (in Japanese). Since he says "Please feel free to copy and paste the code in this article as you like," I modified and published them under the MIT License.

Major features

1. Changed the arguments of solver functions (rk45, dopri5, dop853) so that they can take parameters used in ordinary differential equation (ODE) functions.
   • the parameter had to be set as a global variable before the change
2. Values are calculated up to the specified end time in the SolveOde function, which numerically solves ODEs.
   • If you do something like start_time =+ interval, the data at end time is missing due to decimal rounding error
   • Rust's ode_solvers applies

Solver functions

• rkf45: Runge-Kutta method
• dopri5: Dormand-Prince method order 5
• dop853: Dormand-Prince method order 8

Example

The example in https://zenn.dev/yonda/articles/71aef28aa46fcb (in Japanese)

• $\dfrac{dx_{0}}{dt} = x_{1}$
• $\dfrac{dx_{1}}{dt} = -2\gamma x_{1} - x_{0}$
• parameter values: $\gamma = 0.15$
• initial values: $x_{0} = 1, x_{1} = -0.15$

Import required types and functions

import { TypeFuncRes, TypeParam } from "./solve_ode";
import { SolveOde, rkf45, dopri5, dop853 } from "./solve_ode";

• TypeParam: number[]
• TypeFuncRes: number[]

Define of ordinary differential equations (ODEs)

// Definition of ODE
function func(x: number[], param: TypeParam, _t: number): TypeFuncRes {
    return [
        x[1],                        // dx0/dt = x1
        -2 * param[0] * x[1] - x[0]  // dx1/dt = -2 * param[0] * x1 - x0
    ];
}

Set and parse parameter values

let param = [0.15];
let init = [1, -1.5];

let res = SolveOde(
    func,        // user-defined ODE
    dop853,      // solver function
    param,       // parameters
    0, 20, 0.5,  // start, end, step
    init         // initial values
);
console.log(res);

Execute

# download from repository
npm install
npm run build  # bundle using webpack

node dist/main.js

The type of return values is [number[], number[][]]

• element 1： array of times
• element 2： array of "array of values"

[
  [
     0,  0.5,  1,  1.5,  2,  2.5,  3,  3.5,
     4,  4.5,  5,  5.5,  6,  6.5,  7,  7.5,
     8,  8.5,  9,  9.5, 10, 10.5, 11, 11.5,
    12, 12.5, 13, 13.5, 14, 14.5, 15, 15.5,
    16, 16.5, 17, 17.5, 18, 18.5, 19, 19.5,
    20
  ],
  [ 
    [ 1, -0.15 ],
    [ 0.8166746082016955, -0.557692153141863 ],
    [ 0.4732068547304446, -0.7817998448337315 ],
    [ 0.06999369577839351, -0.796942079229001 ],
    [ -0.29296876631077856, -0.6287833580492583 ],
    [ -0.538764437154819, -0.3410884006508845 ],
    [ -0.6278299171850139, -0.015917620080742143 ],
    [ -0.5617466546837617, 0.2675784748910966 ],
    [ -0.377150240555385, 0.45074951486228504 ],
    [ -0.1325182233446417, 0.5059244391806383 ],
    [ 0.108167684175686, 0.4383875833898941 ],
    [ 0.29073509407040543, 0.2805868154348402 ],
    [ 0.38177114949700197, 0.0809725652433621 ],
    [ 0.37332759332299786, -0.10924683419221558 ],
    [ 0.2811808583957149, -0.24813196381575087 ],
    [ 0.13794049725821486, -0.31125652705202045 ],
    [ -0.01670960459052124, -0.2948214440471942 ],
    [ -0.14601910585511502, -0.21364539900084717 ],
    [ -0.22411810217094255, -0.09520237647253792 ],
    [ -0.24038331741250435, 0.02838757207966796 ],
    [ -0.19972966488592925, 0.12830826343618923 ],
    [ -0.11932845288765788, 0.18513879181538354 ],
    [ -0.02299611928126133, 0.19196035473015535 ],
    [ 0.06514625783123669, 0.15418786007944127 ],
    [ 0.12619953247723414, 0.08662081192625241 ],
    [ 0.1500560037190719, 0.008771314213723642 ],
    [ 0.13647291184074287, -0.060228604569482015 ],
    [ 0.09375352427278882, -0.10592388418793355 ],
    [ 0.03566892159044637, -0.12117145286237656 ],
    [ -0.022434601049273587, -0.10674576554678848 ],
    [ -0.06734406337492452, -0.07005987649144976 ],
    [ -0.09068673306717923, -0.02255531249078119 ],
    [ -0.09015953186782914, 0.023460392555516397 ],
    [ -0.06920720620196623, 0.05773255117331912 ],
    [ -0.03543850777137111, 0.07410487021245042 ],
    [ 0.0016837355195970214, 0.07134826438697033 ],
    [ 0.03325233441033073, 0.052753978829039525 ],
    [ 0.05286346976044077, 0.024755649705834232 ],
    [ 0.05772395744096257, -0.004971149328666756 ],
    [ 0.048783370558624965, -0.029427008029129665 ],
    [ 0.0299968094632241, -0.043785872625261305 ]
  ]
]