Solution of linear and nonlinear singular value problems using operational matrix of integration of Fibonacci wavelets

This article introduces a proficient method for solving both linear and nonlinear second-order singular value differential equations within the framework of Fibonacci wavelets and the collocation technique. Two key theorems are presented to facilitate a discussion on the convergence analysis of the method. The efficacy, ease of application, and computational speed of this approach are demonstrated through its application to diverse problem scenarios. The resulting solutions are compared with existing numerical solutions, further affirming the correctness and effectiveness of the proposed method. Notably, the method consistently yields solutions that align with the exact answers for a multitude of issues. Graphs and figures are employed to visually demonstrate the higher accuracy achieved by the Fibonacci wavelet approach for specific problems. All calculations and data processing are conducted using MATLAB software.