Pointwise Error Estimation for L1 Method in Fractional Time‐Delay Reaction‐Diffusion Equations With Multiple Singularities

ABSTRACT This paper proposes a discrete Laplace transform‐based L1 scheme for fractional time‐delay diffusion‐reaction equations with multiple delay‐induced singularities. A pointwise error analysis establishes that the convergence rate at is , where , is the delay parameter, and is the order of the Caputo derivative. Numerical experiments confirm theoretical predictions and demonstrate the effectiveness of the method in resolving singular behavior between delay interfaces.