Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: An implicit finite difference scheme for solving time-dependent convection dominated diffusion equations in two space variables is presented. A one-sided difference approximation is used for the convection terms and a second-order central difference approximationfor the diffusion term. The implicit scheme is consistent,unconditionally stable and its $L^2$ error estimation is optimal. By preconditioning technique of incremental unknowns, the implicit scheme is an efficient one.
['Lunji Song', 'Yujiang Wu', 'Yang Wang', 'Sa Xie']
I am writing a research paper on a idea An Implicit Finite Difference Scheme with Preconditioning for Convection Dominated Diffusion Equation
[{"from": "human", "value": "I am writing a research paper on a idea An Implicit Finite Difference Scheme with Preconditioning for Convection Dominated Diffusion Equation"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: An implicit finite difference scheme for solving time-dependent convection dominated diffusion equations in two space variables is presented. A one-sided difference approximation is used for the convection terms and a second-order central difference approximationfor the diffusion term. The implicit scheme is consistent,unconditionally stable and its $L^2$ error estimation is optimal. By preconditioning technique of incremental unknowns, the implicit scheme is an efficient one."}]