An adaptation of BICGSTAB for nonlinear biological systems

Here we propose a new adaptation of Van der Vorst's BiCGStab to nonlinear systems, a method combining the iterative features of both sparse linear system solvers, such as BiCGStab, and of nonlinear systems, which in general are linearized by forming Jacobians, and whose resulting system usually involves the use of a linear solver. We consider the feasibility and efficiency of the proposed method in the context of a space-diffusive population model, the growth of which depends nonlinearly on the density itself.