How to double the accuracy of your differential equation approximations
In short: This MIT lecture explores the Midpoint Method, a technique that uses two function evaluations per step to achieve twice the accuracy of Euler's method for solving differential equations.
Presented by Gilbert Strang and Cleve Moler, this session demonstrates how the Midpoint Method improves upon Euler's method. By performing two function evaluations per step, the method offers a significant increase in precision. The lecture uses a nonlinear equation defining the sine function to illustrate these concepts and suggests implementing a related trapezoid method as a further exercise.
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Sources
- Summary by Intellect · source: Midpoint Method, ODE2
- Also: Midpoint Method, ODE2 | MIT Learn
- Also: ocw.mit.edu — Midpoint Method, ODE2 | Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler | Mathematics | MIT OpenCourseWare
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