Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Based on the Lubich's high-order operators, a second-order temporal finite-difference method is considered for the fractional sub-diffusion equation. It has been proved that the finite-difference scheme is unconditionally stable and convergent in L2 norm by the energy method in both one- and two-dimensional cases. The rate of convergence is order of two in temporal direction under the initial value satisfying some suitable conditions. Some numerical examples are given to confirm the theoretical results.
['Zhao-peng Hao', 'Guang Lin', 'Zhi-zhong Sun']
I am writing a research paper on a idea A high-order difference scheme for the fractional sub-diffusion equation
[{"from": "human", "value": "I am writing a research paper on a idea A high-order difference scheme for the fractional sub-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: Based on the Lubich's high-order operators, a second-order temporal finite-difference method is considered for the fractional sub-diffusion equation. It has been proved that the finite-difference scheme is unconditionally stable and convergent in L2 norm by the energy method in both one- and two-dimensional cases. The rate of convergence is order of two in temporal direction under the initial value satisfying some suitable conditions. Some numerical examples are given to confirm the theoretical results."}]