Finite Difference Scheme for Transport-diffusion-reaction of Antibodies in a Tumor : Analysis of Consistency and Stability

According to the mathematical model presented in a scientificité modeling text in the French external agregation competition (public 2008), antibodies are transported between tumors and are reacted with antigens in a transport-diffusion reaction. As a result of the proposed model, an unstable system is produced. Under certain conditions, we propose modifications that result in a new system that is stable and consistent. In this paper, a detailed study of the stability and consistency of this new system is presented, with demonstrations and proofs that are validated numerically.