@article{Wang2024, 
author = {Ziqiang Wang and Jiaojiao Ma and Junying Cao},
title = {A higher-order uniform accuracy scheme for nonlinear    ψ-Volterra integral equations in two dimension with weakly singular kernel},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {6},
pages = {14325-14357},
keywords = {ψ-Volterra integral equations, high-order uniform accuracy scheme, block-by-block method, convergence analysis},
url = {https://www.sciopen.com/article/10.3934/math.2024697},
doi = {10.3934/math.2024697},
abstract = {In this paper, we proposed a higher-order uniform accuracy scheme for nonlinear    ψ-Volterra integral equations in two dimension with weakly singular kernel by using the modified block-by-block method. First, we constructed a high order uniform accuracy scheme method in this paper by dividing the entire domain into some small sub-domains and approximating the integration function with biquadratic interpolation in each sub-domain. Second, we rigorously proved that the convergence order of the higher order uniform accuracy scheme was    O  (      h          s              3      +              σ                  1                      +      h          t              3      +              σ                  2                      ) with    0  <      σ          1        ,      σ          2        <  1 by using the discrete Gronwall inequality. Finally, two numerical examples were used to illustrate experimental results with different values of    ψ to support the theoretical results.}
}