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The program for the dynamics of an infinite system written in MATLAB that solves through implicit trapezoidal integration method has been written. This program is designed to simulate the dynamic processes of complex systems, which involve the use of numerical methods for solving differential equations. The infinite system, which is a fundamental concept in mathematics, is a set of objects that are related in such a way that they form a continuous whole. The use of implicit trapezoidal integration method ensures that the solution of the differential equations is accurate and stable, providing a reliable and efficient way to simulate the dynamic processes of the infinite system. The program can be used in a wide range of fields, including physics, engineering, and finance, to name a few.