Numerical quadrature solution of fractional non-linear Drinfeld-Sokolov-Wilson system

This research mainly concerns obtaining an accurate and efficient numerical solution for fractional nonlinear Drinfeld-Sokolov-Wilson system (DSW). The Doubly Singular Water Wave System (DSW) finds extensive applications across multiple scientific disciplines such as water wave theory, fluid dynamics, quantum mechanics, chemistry, and biological systems. This model is solved using a generalized Liouville-Caputo fractional-order model combined with different approaches of the differential quadrature method. The Newton-Raphson method is used to overcome nonlinearity. To facilitate a deeper understanding of complex physical real-world phenomena, comprehensive graphical analyses and comparative evaluations of the solutions are performed. These results are meticulously plotted by assigning precisely calibrated values to the constant parameters. Such a systematic methodology is widely regarded as a highly compatible and efficient scientific framework for investigating various spacetime fractional models. Ultimately, this approach provides a robust analytical tool for addressing intricate challenges within the fields of engineering and applied physics, effectively bridging the gap between theoretical modeling and practical real-life issues. A MATLAB code is developed to solve this model. A parametric study is also conducted to illustrate the effect of different ways of applying the differential quadrature method, such as the polynomial differential quadrature and the Regularized Shannon Kernel (RSK) The accuracy, convergence and efficiency of proposed techniques are verified.