<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper, we present a Jacobi spectral collocation method to solve nonlinear Volterra-Fredholm integral equations with smooth kernels. The main idea in this approach is to convert the original problem into an equivalent one through appropriate variable transformations so that the resulting equation can be accurately solved using spectral collocation at the Jacobi-Gauss points. The convergence and error analysis are discussed for both <italic>L</italic>∞ and weighted <italic>L</italic>2 norms. We confirm the theoretical prediction of the exponential rate of convergence by the numerical results which are compared with well-known methods.
</abstract>

In this paper, we present a Jacobi spectral collocation method to solve nonlinear Volterra-Fredholm integral equations with smooth kernels. The main idea in this approach is to convert the original problem into an equivalent one through appropriate variable transformations so that the resulting equation can be accurately solved using spectral collocation at the Jacobi-Gauss points. The convergence and error analysis are discussed for both L∞ and weighted L2 norms. We confirm the theoretical prediction of the exponential rate of convergence by the numerical results which are compared with well-known methods.

Solving Nonlinear Volterra-Fredholm Integral Equations using an Accurate Spectral Collocation Method

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

In this paper, we present a Jacobi spectral collocation method to solve nonlinear Volterra-Fredholm integral equations with smooth kernels. The main idea in...

Solving Nonlinear Volterra-Fredholm Integral Equations using an Accurate Spectral Collocation Method

Published Online: Jan 01, 2022

Page range: 35 - 52

Received: Feb 16, 2021

DOI: https://doi.org/10.2478/tmmp-2021-0030

Keywords
Jacobi collocation methods, convergence analysis, spectral methods, nonlinear Volterra-Fredholm integral equations

© 2021 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Solving Nonlinear Volterra-Fredholm Integral Equations using an Accurate Spectral Collocation Method

Published Online: Jan 01, 2022

Page range: 35 - 52

Received: Feb 16, 2021

DOI: https://doi.org/10.2478/tmmp-2021-0030

KeywordsJacobi collocation methods, convergence analysis, spectral methods, nonlinear Volterra-Fredholm integral equations

© 2021 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Jacobi collocation methods, convergence analysis, spectral methods, nonlinear Volterra-Fredholm integral equations