Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A system of coupled nonlinear partial differential equations with convective and dispersive terms was modified from Boussinesq-type equations. Through a special formulation, a system of nonlinear partial differential equations was solved alternately and explicitly in time without linearizing the nonlinearity. Coupled compact schemes of sixth order accuracy in space re developed to obtain numerical solutions. Within couple compact schemes, variables and their first and second derivatives re solved altogether. The sixth order accuracy in space is achieved with a memory-saving arrangement of state variables so that the linear system is banded instead of blocked. This facilitates solving very large systems. The efficiency, simplicity, and accuracy make this coupled compact method viable as variational and ighted residual methods. Results re compared with exact solutions which re obtained via devised forcing terms. Error analyses re carried out, and the sixth order convergence in space and second order convergence in time re demonstrated. Long time integration was also studied to show stability and error convergence rates.
['Don Liu', 'Qin Chen', 'Yifan Wang']
I am writing a research paper on a idea A Sixth Order Accuracy Solution to a System of Nonlinear Differential Equations with Coupled Compact Method
[{"from": "human", "value": "I am writing a research paper on a idea A Sixth Order Accuracy Solution to a System of Nonlinear Differential Equations with Coupled Compact Method"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A system of coupled nonlinear partial differential equations with convective and dispersive terms was modified from Boussinesq-type equations. Through a special formulation, a system of nonlinear partial differential equations was solved alternately and explicitly in time without linearizing the nonlinearity. Coupled compact schemes of sixth order accuracy in space re developed to obtain numerical solutions. Within couple compact schemes, variables and their first and second derivatives re solved altogether. The sixth order accuracy in space is achieved with a memory-saving arrangement of state variables so that the linear system is banded instead of blocked. This facilitates solving very large systems. The efficiency, simplicity, and accuracy make this coupled compact method viable as variational and ighted residual methods. Results re compared with exact solutions which re obtained via devised forcing terms. Error analyses re carried out, and the sixth order convergence in space and second order convergence in time re demonstrated. Long time integration was also studied to show stability and error convergence rates."}]