Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: This work is to provide spectral and pseudo-spectral Jacobi-Galerkin approaches for the second kind Volterra integral equation. The Gauss-Legendre quadrature formula is used to approximate the integral operator and the inner product based on the Jacobi ight is implemented in the ak formulation in the numerical implementation. For some spectral and pseudo-spectral Jacobi-Galerkin methods, a rigorous error analysis in both the infinity and ighted norms is given provided that both the kernel function and the source function are sufficiently smooth. Numerical experiments validate the theoretical prediction.
['Ziqing Xie', 'Xianjuan Li', 'Tao Tang']
I am writing a research paper on a idea Convergence Analysis of Spectral Galerkin Methods for Volterra Type Integral Equations
[{"from": "human", "value": "I am writing a research paper on a idea Convergence Analysis of Spectral Galerkin Methods for Volterra Type Integral Equations"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: This work is to provide spectral and pseudo-spectral Jacobi-Galerkin approaches for the second kind Volterra integral equation. The Gauss-Legendre quadrature formula is used to approximate the integral operator and the inner product based on the Jacobi ight is implemented in the ak formulation in the numerical implementation. For some spectral and pseudo-spectral Jacobi-Galerkin methods, a rigorous error analysis in both the infinity and ighted norms is given provided that both the kernel function and the source function are sufficiently smooth. Numerical experiments validate the theoretical prediction."}]