solving the inverse fisher problem using a discretized teaching-learning-based optimization algorithm

The inverse fisher problem, which involves identifying unknown parameters or functions within the fisher equation, poses a significant challenge due to its ill-posed nature and sensitivity to data noise. in this study, we present an effective numerical approach to solve this inverse problem by combining a fully implicit backward discretization scheme with a discretized version of the teaching-learning-based optimization (tlbo) algorithm. the forward problem is discretized using a fully implicit finite difference method to ensure stability, while the inverse problem is formulated as an optimization task. we adopt a modified and discretized tlbo algorithm based on the framework developed for discrete problems, which has demonstrated strong capabilities in handling discrete and complex optimization tasks. numerical experiments confirm the proposed method’s robustness and accuracy in recovering unknown parameters.