The solution of systems of differential equations plays a crucial role in modeling and
understanding dynamic processes across various disciplines, including physics, engineering,
and finance. the development of innovative algorithms for efficiently solving such systems and
investigates their practical applications in diverse fields. The development of advanced
algorithms tailored for solving systems of differential equations. Emphasis is placed on
numerical techniques, such as Runge-Kutta methods, finite element methods, and adaptive
time-stepping strategies. We delve into the advantages and limitations of each algorithm,
considering factors like stability, convergence, and computational cost.