Numerical Modelling Of Nonlinear And Fractional Diffusion Via Weighted Finite Difference Schemes
Keywords:
Non Linear, Fractional, DiffusionAbstract
This paper presents an unconditionally stable weighted finite difference scheme for a class of nonlinear and fractional diffusion equations. The approach employs fractional-order derivatives in both space and time to derive a generalized convection-diffusion model. By leveraging a modified Grünwald finite difference approximation for the fractional derivatives, the scheme achieves first-order accuracy, unconditional stability, and first-order convergence. To validate the method, error behavior is compared against analytical solutions for benchmark problems, confirming the scheme's convergence properties and practical utility for modelling nonlinear and fractional diffusion.
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