GATE2020: 2

Question

Consider the recursive equation $X_{n+1}=X_n – h(F(X_n)-X_n),$ with initial condition $X_0=1$ and h>0 being a very small valued scalar. This recursion numerically solves the ordinary differential equation ________

• A. $\dot{X}=-F(X), X(0)=1$
• B. $\dot{X}=-F(X)+X, X(0)=1$
• C. $\dot{X}=F(X), X(0)=1$
• D. $\dot{X}=F(X)+X, X(0)=1$