Neurodynamic approaches for solving absolute value equations and circuit implementation

The neurodynamic approaches for solving absolute value equations (AVEs) are studied. By selecting proper adaptive parameters, we propose two neurodynamic approaches: the weakly predefined-time inverse-free neurodynamic approach (WPINA) and the strongly predefined-time gradient neurodynamic approach (SPGNA). Compared to existing neurodynamic approaches for solving AVEs, the upper bounds on the convergence time of WPINA and SPGNA are not only independent of the initial conditions, but also flexible due to the dependency on only one parameter. It is noteworthy that, WPINA and SPGNA have their own advantage. The upper bound on the convergence time of SPGNA is preciser. While the advantage of WPINA is that non-differentiable absolute value term does not need to be smoothed. Additionally, WPINA can degenerate to the inverse-free neurodynamic approach (IFNA) proposed in Chen et al. (2021) when the adaptive parameter is replaced by a constant. Moreover, we introduce the circuit implementation for solving AVEs by using an absolute value circuit. Numerical simulations and an application in boundary value problems demonstrate the effectiveness of the proposed neurodynamic approaches with predefined-time convergence.