Exercise · ZW-RUNGE-KUTTA-METHODS-006 · ★★☆ Intermediate
For \(y'=2y\), \(y(0)=1\) and \(h=0.5\), what is \(y_1\) using Euler's method?
Choose one option.
Show answer
- B. \(2\)
Explanation
Euler gives \(y_1=y_0+h\cdot 2y_0=1+0.5\cdot 2=2\), using \(f(t,y)=2y\) with \(y_0=1\).
Review the concept: Runge-Kutta methods
Runge-Kutta methods are families of one-step numerical schemes that approximate the solution of an initial value problem by evaluating the function \(f\) at several intermediate points within each step.
\[y_{n+1}=y_n+h\sum_{i=1}^{s} b_i k_i\]
More practice problems: runge-kutta methods
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- ZW-RUNGE-KUTTA-METHODS-004 In an explicit Runge-Kutta method, what shape does the coefficient matrix a_ij have?
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