Saad, Khaled M.Srivastava, Rekha2024-05-022024-05-022024Saad, K. M., & Srivastava, R. (2024). Non-standard finite difference and Vieta-Lucas orthogonal polynomials for the multi-space fractional-order coupled Korteweg-de Vries equation. Symmetry, 16(2), 242. https://doi.org/10.3390/sym16020242https://doi.org/10.3390/sym16020242https://hdl.handle.net/1828/16467This paper focuses on examining numerical solutions for fractional-order models within the context of the coupled multi-space Korteweg-de Vries problem (CMSKDV). Different types of kernels, including Liouville-Caputo fractional derivative, as well as Caputo-Fabrizio and Atangana-Baleanu fractional derivatives, are utilized in the examination. For this purpose, the nonstandard finite difference method and spectral collocation method with the properties of the Shifted Vieta-Lucas orthogonal polynomials are employed for converting these models into a system of algebraic equations. The Newton-Raphson technique is then applied to solve these algebraic equations. Since there is no exact solution for non-integer order, we use the absolute two-step error to verify the accuracy of the proposed numerical results.enAttribution 4.0 InternationalArticleDepartment of Mathematics and Statistics