Euler Method Calculator

How to Use the Euler Method Calculator

This Euler Method Calculator is a powerful tool designed to numerically approximate solutions to first-order differential equations. Follow the steps below to effectively use this calculator.

Step 1: Enter Initial Values

• Initial Value (y₀): Enter the initial value of y. This is the starting point of the dependent variable, usually provided by the problem statement.
• Initial Time (t₀): Enter the initial value of t. This is the time corresponding to the initial value of y.

Step 2: Define the Time Interval

• Final Time (tₙ): Input the final time where you want to approximate the value of y. The calculator will use this as the endpoint for the Euler method.
• Step Size (h): Specify the step size. This determines the increment of t for each iteration of the Euler method.

Step 3: Select the Differential Equation

• Select Differential Equation: Choose one of the pre-defined differential equations for which you wish to find the numerical solution. The available options are:
  • dy/dt = t + y
  • dy/dt = t² + y
  • dy/dt = e^t + y

Step 4: Calculate Results

• Number of Steps: The calculator will automatically compute the number of steps based on the provided time interval and step size.
• Approximate Value (yₙ): This field will display the approximate value of yₙ using the Euler method with the given parameters.
• Local Truncation Error: The calculator will estimate the truncation error incurred in a single step of the Euler method.
• Global Truncation Error: This will provide an estimate of the cumulative error over the entire interval.

Follow these steps carefully to obtain the numerical solutions you need. Ensure the inputs provided are within the acceptable bounds and format to achieve accurate and meaningful results.