Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: An integrating factor mixed with Runge-Kutta technique is a time integration method that can be efficiently combined with spatial spectral approximations to provide a very high resolution to the smooth solutions of some linear and nonlinear partial differential equations. , the novel hybrid Fourier-Galerkin Runge-Kutta scheme, with the aid of an integrating factor, is proposed to solve nonlinear high-order stiff PDEs. Error analysis and properties of the scheme are provided. Application to the approximate solution of the nonlinear stiff Korteg-de Vries (the 3rd order PDE, dispersive equation), Kuramoto-Sivashinsky (the 4th order PDE, dissipative equation) and Kawahara (the 5th order PDE) equations are presented. Comparisons are made beten this proposed scheme and the competing method given by Kassam and Trefethen. It is found that for KdV, KS and Kawahara equations, the proposed method is the best.
['N. Vaissmoradi', 'Alaeddin Malek', 'S.H. Momeni-Masuleh']
I am writing a research paper on a idea Error analysis and applications of the Fourier-Galerkin Runge-Kutta schemes for high-order stiff PDEs
[{"from": "human", "value": "I am writing a research paper on a idea Error analysis and applications of the Fourier-Galerkin Runge-Kutta schemes for high-order stiff PDEs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: An integrating factor mixed with Runge-Kutta technique is a time integration method that can be efficiently combined with spatial spectral approximations to provide a very high resolution to the smooth solutions of some linear and nonlinear partial differential equations. , the novel hybrid Fourier-Galerkin Runge-Kutta scheme, with the aid of an integrating factor, is proposed to solve nonlinear high-order stiff PDEs. Error analysis and properties of the scheme are provided. Application to the approximate solution of the nonlinear stiff Korteg-de Vries (the 3rd order PDE, dispersive equation), Kuramoto-Sivashinsky (the 4th order PDE, dissipative equation) and Kawahara (the 5th order PDE) equations are presented. Comparisons are made beten this proposed scheme and the competing method given by Kassam and Trefethen. It is found that for KdV, KS and Kawahara equations, the proposed method is the best."}]