Euler Method:
The Euler method is a simple numerical method for solving ordinary differential equations (ODEs). It is a first-order method that uses a finite difference approximation to approximate the derivative of the function at each step. The method is based on the idea of approximating the solution curve by a series of line segments.

Improved Euler Method:
The Improved Euler method, also known as the Heun's method, is an extension of the Euler method. It is a second-order method that improves the accuracy of the approximation by using a midpoint estimate for the derivative at each step. It involves two stages: an Euler step to estimate the slope at the beginning of the interval, and a midpoint step to estimate the slope at the midpoint of the interval.

Runge-Kutta Method:
The Runge-Kutta method is a popular numerical method for solving ordinary differential equations. It is a family of methods that use a weighted average of several different estimates of the derivative at each step. The most commonly used variant is the fourth-order Runge-Kutta method (RK4), which involves four function evaluations per step.

Adams-Moulton Method:
The Adams-Moulton method is a multi-step numerical method for solving ordinary differential equations. It is an extension of the Adams-Bashforth method, which is a predictor-corrector method that uses a combination of forward differences and backward differences to approximate the derivative at each step. The Adams-Moulton method improves the accuracy of the approximation by using a backward difference formula to calculate the derivative at the next step.

Conclusion:
Among the given options, the Adams-Moulton method is the multi-step numerical method for solving ordinary differential equations. It is a higher-order method that provides more accurate approximations compared to the Euler method, Improved Euler method, and Runge-Kutta method. The Adams-Moulton method is particularly useful for solving stiff differential equations, where the step size needs to be small to maintain stability.