Abstract
This article looks into the use of the fourth-order Runge-Kutta (RK4) method in realistic motion simulation within computer graphics. With dynamic animations, there is an emerging need to solve physical systems using ordinary differential equations, for which RK4 is particularly useful due to its accuracy, stability, and balanced computational cost and efficiency. We implement motion phenomena with damped spring-mass systems by changing second-order differential equations into first-order systems that can be integrated using RK4. The results are measured against Euler and Midpoint methods for assessing stability, error control, and visual smoothness. In every instance, RK4 was found to be the most accurate, stable, and free from overshoot and jitter artifacts. The method demonstrates its effectiveness in real-time animation simulation, including but not limited to simulating cloth movement, flexible body motion, and character dynamic movements through progressive simulation and case studies. Even after undergoing extensive simulation durations, RK4 repeated proved to be supremely reliable regarding energy conservation, damping precision, and fidelity. While perhaps more costly in terms of computation than the more straightforward methods, RK4 remains highly tenable with today's processing capabilities. In addition to greatly improving the physics realism in simulations, the method is commendably applicable in Unity and PhysX or Bullet visual engines. The study illustrates smooth and realistic animation with the help of RK4 while further establishing its importance as a fundamental method for motion graphics and simulation in academic research and industry use.