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Volume 9, Issue 1
Multistep Collocation Methods for Volterra Integral Equations with Weakly Singular Kernels

Jingjun Zhao, Teng Long & Yang Xu

DOI: 10.4208/eajam.030118.070518

East Asian J. Appl. Math., 9 (2019), pp. 67-86.

Published online: 2019-01

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  • Abstract

A multistep collocation method on uniform grids for weakly singular Volterra integral equations is considered. The initial integral equation is modified by a smoothing transformation and then solved by a multistep collocation method on a uniform grid. Convergence and linear stability are also studied. Numerical results demonstrate the efficiency of the method.

  • Keywords

Multistep collocation method, Volterra integral equation, weakly singular kernel.

  • AMS Subject Headings

65L20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-9-67, author = {Jingjun Zhao, Teng Long and Yang Xu}, title = {Multistep Collocation Methods for Volterra Integral Equations with Weakly Singular Kernels}, journal = {East Asian Journal on Applied Mathematics}, year = {2019}, volume = {9}, number = {1}, pages = {67--86}, abstract = {

A multistep collocation method on uniform grids for weakly singular Volterra integral equations is considered. The initial integral equation is modified by a smoothing transformation and then solved by a multistep collocation method on a uniform grid. Convergence and linear stability are also studied. Numerical results demonstrate the efficiency of the method.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.030118.070518}, url = {http://global-sci.org/intro/article_detail/eajam/12935.html} }
TY - JOUR T1 - Multistep Collocation Methods for Volterra Integral Equations with Weakly Singular Kernels AU - Jingjun Zhao, Teng Long & Yang Xu JO - East Asian Journal on Applied Mathematics VL - 1 SP - 67 EP - 86 PY - 2019 DA - 2019/01 SN - 9 DO - http://doi.org/10.4208/eajam.030118.070518 UR - https://global-sci.org/intro/article_detail/eajam/12935.html KW - Multistep collocation method, Volterra integral equation, weakly singular kernel. AB -

A multistep collocation method on uniform grids for weakly singular Volterra integral equations is considered. The initial integral equation is modified by a smoothing transformation and then solved by a multistep collocation method on a uniform grid. Convergence and linear stability are also studied. Numerical results demonstrate the efficiency of the method.

Jingjun Zhao, Teng Long and Yang Xu. (2019). Multistep Collocation Methods for Volterra Integral Equations with Weakly Singular Kernels. East Asian Journal on Applied Mathematics. 9 (1). 67-86. doi:10.4208/eajam.030118.070518
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