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A space-time spectral approximation for solving nonlinear variable-order fractional convection-diffusion equations with nonsmooth solutions

    https://doi.org/10.1142/S0129183123500419Cited by:4 (Source: Crossref)

    One of the problems in the numerical analysis of solutions is the nonlinear variable-order fractional convection-diffusion equations for nonsmooth solutions. We offer a numerical technique based on the shifted Legendre Gauss-Lobatto collocation and the shifted Chebyshev Gauss-Radau collocation to solve the problem. The technique with shifted Legendre Gauss-Lobatto and shifted Chebyshev Gauss-Radau nodes is applied to diminish nonlinear variable-order fractional convection-diffusion equations to an easily-solvable system of algebraic equations. Besides, we give numerical test examples to show that the approach can preserve the nonsmooth solution of the underlying problems.

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