Abstract:

Quadratic ordinary differential equations (ODEs) are a class of second-order differential equations that appear in various scientific and engineering applications. Solving these equations analytically can be challenging, especially when closed-form solutions are not readily available. Therefore, numerical methods play a vital role in approximating solutions to quadratic ODEs. This paper presents a comprehensive review of various numerical approaches employed for solving quadratic ODEs, including finite difference methods, Runge-Kutta methods, and spectral methods. Theoretical foundations, algorithmic details, and computational considerations are discussed, along with comparative analyses of their accuracy, efficiency, and applicability. The paper aims to provide researchers and practitioners with insights into selecting appropriate numerical techniques based on the specific characteristics of the quadratic ODEs they encounter.

Description:

Numerical methods, quadratic ordinary differential equations, finite difference methods, Runge-Kutta methods, spectral methods, accuracy, efficiency