Operator Splitting for System of Differential Equations

Linear system of differential and partial equations with varying coefficients is widely used by a number of scientific and engineering areas. Therefore, developing and using high accurate numerical methods is important. In this work basic idea of operator splitting methods is discussed. Operator splitting method is widely used numerical method for solving those kind of equations. First and second order operator splitting methods are discussed for Ordinary differential equations. Then, application of methods are show in case of partial differential equations, on the example of convection-diffusion and reaction-diffusion equations.