11. Heun’s Method
Numerical methods play a crucial role in solving ordinary differential equations (ODEs) that cannot be solved analytically. Heun's Method, also known as the improved Euler's method, offers a second-order technique that enhances accuracy by averaging slopes at the beginning and end of intervals. This method is essential in engineering applications where precision is vital.
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What we have learnt
- Heun’s Method is a second-order improvement over Euler’s method for numerically solving ODEs.
- It utilizes a predictor-corrector approach to refine estimates by averaging slopes.
- Heun's Method balances efficiency and accuracy, making it suitable for a variety of engineering applications.
Key Concepts
- -- Ordinary Differential Equations (ODEs)
- Equations involving functions and their derivatives which describe how a quantity changes over time.
- -- Heun's Method
- A numerical technique that improves upon Euler's method by using an average of slopes to enhance accuracy.
- -- PredictorCorrector
- A two-step process in numerical analysis where an initial estimate is refined to improve accuracy.
- -- Stability
- A measure of how errors in numerical solutions behave as they propagate through calculations.
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