Optimization of Civil Engineering Initial Value Problems by Particle Swarm Optimization Algorithm

A differential equation is a mathematical equation that relates some function with its derivatives. In applications, the functions usually represent physical quantities, the derivatives represent their rates of change, and the equation defines a relationship between the two. Because such relations are extremely common, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. They are useful in many domains. Traditionally, Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) can be solved by classical mathematical methods, which are not very precise namely in the difficult problems. Swarm Intelligence Algorithms are considerate a crucial factor of modern optimization when large sort of Nature Inspired Algorithms have emerged recently to treaty successfully a variety of problems. In this paper, Particle Swarm Optimization Algorithm (PSO) is used to solve approximately an (IVP), by a selected example; the efficiency of the considered method is verified by means of a simulation study compared by a Runge Kutta method that shows very good results.