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Numerical ODE: Euler, Runge–Kutta

Why this is asked: Know the local vs global order (Euler: local O(h²), global O(h)), the RK2 order conditions, and the stability interval for Euler applied to y′ = λy.

Numerical methods for ODE

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Order of a method, and the step size stability forces on youinteractive

Why explicit Euler needs h < 2/|λ| however accurate you wanted to be.

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Using Euler's method with step size 0.05, the approximate value of the solution of dy/dx $= \sqrt{3x + 2y + 1}, y(1) = 1$ , at x = 1.1 (rounded to two decimal places) is

Next: Euler–Lagrange equation and standard functionals

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Open this in the full syllabus view · Unit 3