euler method in javascript

To implement the Euler method in JavaScript, you can follow these steps:

1. Define your differential equation as a JavaScript function. For example, let's consider the first-order differential equation dy/dt = f(t, y).

index.tsx
function f(t, y) {
  return 2 * t + y;
}
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2. Write a function that implements the Euler method. This function should take the initial conditions, the step size, and the number of iterations as inputs, and return an array with the values of t and y at each iteration.

index.tsx
function eulerMethod(y0, t0, h, n) {
  let t = t0;
  let y = y0;
  let result = [{ t, y }];

  for (let i = 1; i <= n; i++) {
    t = t0 + i * h;
    y = y + h * f(t, y);
    result.push({ t, y });
  }

  return result;
}
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3. Call the eulerMethod function with the desired inputs to obtain the numerical solution. For example, if we want to solve dy/dt = 2t + y with the initial condition y(0) = 1, a step size of h = 0.1, and 10 iterations, we can do:

index.tsx
let solution = eulerMethod(1, 0, 0.1, 10);

console.log(solution);
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This will print an array of objects representing the values of t and y at each iteration.

Note: Keep in mind that the Euler method has limitations and may produce less accurate results compared to more advanced numerical methods.