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Legendre polynomials' first derivatives have been used as the basis function via the pseudo-Galerkin spectral method. Operational matrices for derivatives have been used and extended to deal with the system of ordinary differential-algebraic equations. An algorithm via those matrices has been designed. The accuracy and efficiency of the proposed algorithm had been shown by two techniques, theoretically, via the boundedness of the approximated expansion and numerically through numerical examples. [ABSTRACT FROM AUTHOR]

A new generalized KdV equation, describing the motions of long waves in shallow water under the gravity field, is considered in this paper. By adopting a series of well-organized methods, the Bäcklund transformation, the bilinear form and diverse wave structures of the governing model are formally extracted. The exact solutions listed in this paper are categorized as lump-type, complexiton, and soliton solutions. To exhibit the physical mechanism of the obtained solutions, several graphical illustrations are given for particular choices of the involved parameters. As a direct consequence, diverse wave structures given in this paper enrich the studies on the KdV-type equations. [ABSTRACT FROM AUTHOR]

In this paper, we have investigated women's malignant disease, cervical cancer, by constructing the compartmental model. An extended fractal–fractional model is used to study the disease dynamics. The points of equilibria are computed analytically and verified by numerical simulations. The key role of R 0 in describing the stability of the model is presented. The sensitivity analysis of R 0 for deciding the role of certain parameters altering the disease dynamics is carried out. The numerical simulations of the proposed numerical technique are demonstrated to test the claimed facts. [ABSTRACT FROM AUTHOR]