@article{Wang2023, 
author = {Ziqiang Wang and Qin Liu and Junying Cao},
title = {A higher-order numerical scheme for system of two-dimensional nonlinear fractional Volterra integral equations with uniform accuracy},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {6},
pages = {13096-13122},
keywords = {nonlinear Volterra integral equation system, higher-order numerical scheme, convergence analysis},
url = {https://www.sciopen.com/article/10.3934/math.2023661},
doi = {10.3934/math.2023661},
abstract = {We give a modified block-by-block method for the nonlinear fractional order Volterra integral equation system by using quadratic Lagrangian interpolation based on the classical block-by-block method. The core of the method is that we divide its domain into a series of subdomains, that is, block it, and use piecewise quadratic Lagrangian interpolation on each subdomain to approximate        κ    (  x  ,  y  ,  s  ,  r  ,  u  (  s  ,  r  )  ). Our proposed method has uniform accuracy and its convergence order is    O  (      h    x          4      −      α        +      h    y          4      −      β        ). We give a strict proof for the error analysis of the method, and give several numerical examples to verify the correctness of the theoretical analysis.}
}