Numerical Solutions of Some Weak Singular Nonlinear Integral Equations of The First Type Using The Spectral Collocation Method
Year: 2024
Type: article
Abstract: In this paper, a collocation-spectral approximation is proposed for weakly nonlinear and neutral singular Volterra integral-differential equations with rough solutions. We used some appropriate transformations to transform the equation of the equation into a new equation, so that the solution of the new equation has a better order (smoothness) and Jacobi's orthogonal polynomial theory can be easily used. Under appropriate assumptions on the nonlinear part, we were able to perform an acceptable error analysis on the soft and the weighted soft. To obtain a numerical approximation, some numerical examples (linear and non-linear) with uneven solutions are considered and numerical results are also presented. Also, a comparison between the proposed method and some existing numerical methods is also provided.
Institution: Islamic Azad University, Tehran
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4403231420