Euler's Method Calculator
Approximate the solution of a first-order ordinary differential equation using Euler's method. Enter the differential equation, initial condition, step size, and number of steps.
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isCalculator Editorial Team
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How to Use Euler's Method Calculator
This calculator approximates the solution to a first-order differential equation y' = f(x, y) with initial condition y(x₀) = y₀ using Euler's method.
- Enter f(x, y): Type the right-hand side of your ODE using JavaScript syntax (e.g.,
x + y,Math.sin(x) + Math.exp(y)). - Set initial conditions: Provide x₀ and y₀ (the starting point).
- Choose step size (h): A positive number (e.g., 0.1). Smaller values give more accuracy but more steps.
- Set number of steps (n): How many iterations to perform (max 1000). The final x will be x₀ + n·h.
- Click "Calculate": The result shows the approximate y at the final x, plus a table with all intermediate steps.
Note: All numeric inputs accept decimals. The function must return a number; use Math. for advanced functions (e.g., Math.log(x)).
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Frequently Asked Questions
Euler's method is a numerical technique to approximate the solution of an ordinary differential equation given an initial value. It uses the slope at the current point to step forward.
Use JavaScript syntax. For example, x + y, Math.sin(x) * y, or Math.exp(x) + y. Variables must be x and y.
Ensure all inputs are valid numbers, step size and number of steps are positive, and the function is correctly defined. The function must return a number.
