IB DP Maths: AI HL复习笔记5.6.4 Approximate Solutions to Differential Equations
Euler’s Method: First Order
What is Euler’s method?
- Euler’s method is a numerical method for finding approximate solutions to differential equations
- It treats the derivatives in the equation as being constant over short ‘steps’
- The accuracy of the Euler’s Method approximation can be improved by making the step sizes smaller
How do I use Euler’s method with a first order differential equation?
Exam Tip
- Be careful with letters – in the equations in the exam, and in your GDC’s recursion calculator, the variables may not be x and y
- If an exam question asks you how to improve an Euler’s method approximation, the answer will almost always have to do with decreasing the step size!
Worked Example
b)Explain how the accuracy of the approximation in part (a) could be improved.
Euler's Method: Coupled Systems
How do I use Euler’s method with coupled first order differential equations?
Exam Tip
- Be careful with letters – in the equations in the exam, and in your GDC’s recursion calculator, the variables may not be x, y and t.
- If an exam question asks you how to improve an Euler’s method approximation, the answer will almost always have to do with decreasing the step size!
Worked Example
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