Question

A multistep method for solving a differential equation numerically among the following is

• A. Runge-Kutta method
• B. Euler's method
• C. Successive approximation method
• D. Adams-Bashforth method

Hint:

Common numerical methods: \[ \boxed{ \begin{aligned} &\text{Euler} &&\rightarrow \text{Single-step} &\text{Runge-Kutta} &&\rightarrow \text{Single-step} &\text{Adams-Bashforth} &&\rightarrow \text{Multi-step} \end{aligned} } \] Adams-Bashforth uses values from previous steps to compute the next approximation.

Answer 1

The Correct Option is D

Step 1: Recall the classification of numerical methods. Numerical methods for solving ordinary differential equations are classified as \[ \begin{aligned} &\text{Single-step methods}, &\text{Multi-step methods}. \end{aligned} \]

Step 2: Identify the multistep method. Among the given methods,
• Euler's method is a single-step method.
• Runge-Kutta methods are single-step methods.
• Successive approximation is an iterative analytical technique.
• Adams-Bashforth method is a multistep predictor method. Hence, \[ \boxed{\text{Adams-Bashforth method}} \] is the correct answer. Thus, \[ \boxed{(D)} \] is the correct answer.