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CSS Applied Mathematics QUESTION #1312
Question 1
Euler's method for the IVP \(y'=f(x,y)\), \(y(x_0)=y_0\) with step size \(h\) gives:
  • \(y_{n+1}=y_n+hf(x_n,y_n)\)✔️
  • \(y_{n+1}=y_n+\dfrac{h}{2}[f(x_n,y_n)+f(x_{n+1},y_{n+1})]\)
  • \(y_{n+1}=y_n-hf(x_n,y_n)\)
  • \(y_{n+1}=y_n+h^2f(x_n,y_n)\)
Correct Answer Explanation
Euler's (forward Euler) method: \(y_{n+1}=y_n+h\cdot f(x_n,y_n)\). It is a first-order method derived from the Taylor series truncated after the first derivative term. The local truncation error is \(O(h^2)\) and global error is \(O(h)\).