(untitled) (European Journal of Pure and Applied Mathematics, 2025)
This study investigates two ways of discussing the solution of linear, mixed, and special nonlinear models of second-order differential equations: the differential transform method and the generalized Fibonacci collocation method. The differential transform method uses a step-by-step approach to convert differential equations and their conditions into power series, giving an exact or highly accurate solution. On the other hand, the generalized Fibonacci collocation method transforms the problem into a system of equations with unknown coefficients, which are determined by solving this system using matrix operations. It yields a numerical solution. We discuss convergence and error bounds of generalized Fibonacci polynomials in detail. This study evaluates the solutions of four different problems, focusing on their reliability and accuracy. This comparison shows that our algorithms are efficient.