Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  introduce and comment some recent efficient solvers for time dependent partial differential or ordinary differential problems, considering both linear and nonlinear cases. Here “efficient” may have different meanings, for instance a computational complexity which is better than standard time advance schemes as ll as a strong parallel efficiency, especially parallel-in-time capability. More than a review,  will try to show the close links beten the different approaches and set up a general framework that will allow us to combine the different approaches for more efficiency. As a complementary aspect,  will also discuss ways to include reduced-order models and fast approximate exponential integrators as fast global solvers. For developments and discussion,  will mainly focus on the heat equation, in both linear and nonlinear form.
['Florian De Vuyst']
I am writing a research paper on a idea Efficient solvers for time-dependent problems: a review of IMEX, LATIN, PARAEXP and PARAREAL algorithms for heat-type problems with potential use of approximate exponential integrators and reduced-order models
[{"from": "human", "value": "I am writing a research paper on a idea Efficient solvers for time-dependent problems: a review of IMEX, LATIN, PARAEXP and PARAREAL algorithms for heat-type problems with potential use of approximate exponential integrators and reduced-order models"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  introduce and comment some recent efficient solvers for time dependent partial differential or ordinary differential problems, considering both linear and nonlinear cases. Here \u201cefficient\u201d may have different meanings, for instance a computational complexity which is better than standard time advance schemes as ll as a strong parallel efficiency, especially parallel-in-time capability. More than a review,  will try to show the close links beten the different approaches and set up a general framework that will allow us to combine the different approaches for more efficiency. As a complementary aspect,  will also discuss ways to include reduced-order models and fast approximate exponential integrators as fast global solvers. For developments and discussion,  will mainly focus on the heat equation, in both linear and nonlinear form."}]