Error analysis of Jacobi–Galerkin method for solving weakly singular Volterra–Hammerstein integral equations

ABSTRACT

In this article, Jacobi spectral Galerkin method and its iterated version are developed for second kind weakly singular Volterra–Hammerstein integral equations. We transform the domain of integration from $[0,t]$ to $[-1,1]$ by using variable and function transformations so that the theory of Jacobi polynomials can be applied and obtain the superconvergence results. Further, we enhance these superconvergence results in iterated Jacobi spectral multi-Galerkin method. We verify the theoretical results by numerical examples.

Keywords:

• Volterra integral equations
• weakly singular kernels
• Jacobi polynomials
• spectral Galerkin method
• superconvergence rates
• multi-Galerkin method

2010 Mathematics Subject Classifications:

• 45B05
• 45G10
• 65R20

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research work of Gnaneshwar Nelakanti was supported by the National Board for Higher Mathematics, India, research project: 02011/6/2019NBHM(R.P)/R & D II /1236 dated 28/1/2