Class Solver

Main features

• First, second and third order non-linear solving
• Bufferization of result for best performance

Getting started

A solver is an object that models an ode between any object of type Vector. The equation has the following form

Where u is an unknown vector valued function and f a smooth time dependant vector field.

Initialize a solver

Solver objects are initialized with the value of the initial condition u0, the function f and the time step dt Therefore to initialize a solver, simply choose values of theses parameters that models your problem.

Example

let f = u => u; // equation du/dt = u first order linear equation
let dt = 0.1; // time step
let u0 = new Vector3(1, 0, 0); // initial condition
let solver = new Solver(f, dt, u0),
console.log(solver.dt) // prints 0.1

Solve equations

Once you've initialized the solver, you can start compute solutions of your equation. There is two ways to do that :

• Compute values step-by-step
• Compute value after a maximum duration

let u = solver.step();
let v = solver.solve(tmax);

You can change initial condition and time step each time you call step and solve methods.

let u0 = Vector3(2, 3, 7);
let dt = 0.1;
let u = solver.step(u0, dt);

Note currently only Euler's explicit method is provided.

Time dependant equations

Time dependant equations uses the member t to count time from the last initialisation/reset of the solver. Each time an equation is solved, t is set to it's final value after solving. If you want to reset the value of t, call the reset method.