@Article{cmes.2023.030449,
AUTHOR = {Tao Hu, Cheng Huang, Sergiy Reutskiy, Jun Lu, Ji Lin},
TITLE = {A Novel Accurate Method for Multi-Term Time-Fractional Nonlinear Diffusion Equations in Arbitrary Domains},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {138},
YEAR = {2024},
NUMBER = {2},
PAGES = {1521--1548},
URL = {http://www.techscience.com/CMES/v138n2/54632},
ISSN = {1526-1506},
ABSTRACT = {A novel accurate method is proposed to solve a broad variety of linear and nonlinear (1+1)-dimensional and (2+1)-
dimensional multi-term time-fractional partial differential equations with spatial operators of anisotropic diffusivity. For (1+1)-dimensional problems, analytical solutions that satisfy the boundary requirements are derived.
Such solutions are numerically calculated using the trigonometric basis approximation for (2+1)-dimensional
problems. With the aid of these analytical or numerical approximations, the original problems can be converted
into the fractional ordinary differential equations, and solutions to the fractional ordinary differential equations
are approximated by modified radial basis functions with time-dependent coefficients. An efficient backward
substitution strategy that was previously provided for a single fractional ordinary differential equation is then used
to solve the corresponding systems. The straightforward quasilinearization technique is applied to handle nonlinear
issues. Numerical experiments demonstrate the suggested algorithm’s superior accuracy and efficiency.},
DOI = {10.32604/cmes.2023.030449}
}