Intermediate boundary conditions in operator-splitting techniques and linearization methods

摘要

The intermediate boundary conditions for the solution of linear, one-dimensional reaction-diffusion equations have been determined analytically for the case that the reaction and diffusion operators are solved once each in each time step. These boundary conditions have been used to solve systems of nonlinear, one-dimensional reaction-diffusion equations by means of linearized θ-methods and time-linearized techniques which are based on the linearization of the nonlinear algebraic and differential, respectively, equations of the reaction operator; both techniques provide analytical solutions to the reaction operator although in discrete and continuous forms, respectively. Since the linearization of reaction operators may result in dense Jacobian matrices, diagonally and triangularly linearized techniques which uncouple or couple in a sequential manner, respectively, the dependent variables are proposed. It is shown that the accuracy of time-linearized methods is higher than that of linearized θ-techniques, whereas the accuracy of both linearization methods deteriorates as the coupling between dependent variables is weakened.