Computational half-sweep explicit group Gauss–Seidel method with Caputo nonlocal arithmetic-mean approach for nonlinear time-fractional diffusion equation

This paper introduces the half-sweep 4-Point Explicit Group Gauss–Seidel (HS4EGGS) method combined with a half-sweep Caputo nonlocal arithmetic-mean discretisation for solving nonlinear time-fractional diffusion equations (NTFDEs).  Designed to enhance computational efficiency and accuracy, this approach minimizes iteration counts through a half-sweep iteration strategy and accurately represents memory and hereditary properties intrinsic to fractional derivatives.  The HS4EGGS method significantly reduces computational costs while maintaining precision, making it particularly suited for large-scale problems.  Numerical experiments compare HS4EGGS with FS4EGGS and FSGS methods, demonstrating its superior performance in convergence speed and accuracy across varying fractional orders and mesh sizes.  For instance, HS4EGGS consistently outperforms the other methods in terms of iteration count and computational time while delivering solutions that align closely with expected results.  This study highlights the robustness of HS4EGGS, positioning it as a reliable and efficient method for solving NTFDEs, with potential applications across diverse scientific and engineering domains.