Research Projects

This study investigates numerical solutions for nonlinear mathematical models like ordinary differential equations (ODEs), partial differential equations (PDEs), and fractional PDEs using a generalized operational matrix of integration via continuous wavelets. Nonlinear models are unpredictable and require a simple numerical method based on the continuous wavelet operational matrix of integration. The main idea is to generate the operational matrix of integration and convert nonlinear mathematical models into a system of nonlinear algebraic equations using the matrix's properties. Newton's method is used to solve this system, yielding unknown coefficients that contribute to the wavelet-based numerical solution for corresponding models. The efficiency of the proposed technique is tested by comparing the results with other literature methods.