Operator splitting and error analysis in malaria modeling

Abstract

In this investigation, operator splitting techniques have been leveraged successfully to get better accuracy of the numerical solution of a system of nonlinear ordinary differential equations representing the propagation of malaria disease as a test problem. Simulated split solutions using different operator splitting schemes, namely, the sequential splitting scheme and the Strang-Marchuk splitting scheme are compared with the non-split reference solution. The order and accuracy of the methods have been derived analytically and by a numerical experiment for the test problem. We have also calculated the numerical errors associated with the methods. Moreover, the superiority of the splitting scheme over some non-split schemes in terms of computational time for a fixed global error has been established. For quantitative insight, a thorough large-scale numerical simulation has been performed and the predicted results are presented graphically.