Numerical treatment of nonlinear model of virus propagation in computer networks: an innovative evolutionary Padé approximation scheme

Abstract

This work proposes a novel mesh free evolutionary Padé approximation (EPA) framework for obtaining closed form numerical solution of a nonlinear dynamical continuous model of virus propagation in computer networks. The proposed computational architecture of EPA scheme assimilates a Padé approximation to transform the underlying nonlinear model to an equivalent optimization problem. Initial conditions, dynamical positivity and boundedness are dealt with as problem constraints and are handled through penalty function approach. Differential evolution is employed to obtain closed form numerical solution of the model by solving the developed optimization problem. The numerical results of EPA are compared with finite difference schemes like fourth order Runge–Kutta (RK-4), ODE45 and Euler methods. Contrary to these standard methods, the proposed EPA scheme is independent of the choice of step lengths and unconditionally converges to true steady state points. An error analysis based on residuals witnesses that the convergence speed of EPA is higher than a globally convergent non-standard finite difference (NSFD) scheme for smaller as well as larger time steps.