A multiple iterative splitting method for higher order differential equations

This paper presents an extension of standard iterative splitting schemes to multiple splitting schemes for solving higher order differential equations. The motivation is to solve the systems of equations which occur in the dynamics of electrons in a plasma, using a simplified Boltzmann equation with scattering terms. We reformulate its integro-differential equations into higher order differential equations and then apply iterative splitting methods. Such methods allow decoupling the system into simpler and more quickly solvable first order differential equations: the main idea is to separate the fundamental system of the higher order differential equations into subsystems. This decomposition of the system into first order differential equations allows analyzing such schemes and deriving numerical algorithms. In the numerical part, we discuss the motivation from physical applications in plasma dynamics and present numerical simulations for real-life applications of these integro-differential models.