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Volume 3, Issue 4
Crank-Nicolson Quasi-Wavelet Based Numerical Method for Volterra Integro-Differential Equations on Unbounded Spatial Domains

Man Luo, Da Xu & Limei Li

DOI: 10.4208/eajam.170813.131013a

East Asian J. Appl. Math., 3 (2013), pp. 283-294.

Published online: 2018-02

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  • Abstract

The numerical solution of a parabolic Volterra integro-differential equation with a memory term on a one-dimensional unbounded spatial domain is considered. A quasi-wavelet based numerical method is proposed to handle the spatial discretisation, the Crank-Nicolson scheme is used for the time discretisation, and second-order quadrature to approximate the integral term. Some numerical examples are presented to illustrate the efficiency and accuracy of this approach.

  • Keywords

Parabolic Volterra integro-differential equation, unbounded spatial domain, quasi-wavelet, Crank-Nicolson method.

  • AMS Subject Headings

35R09 , 45K05, 65M99, 65T60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-3-283, author = {Man Luo, Da Xu and Limei Li}, title = {Crank-Nicolson Quasi-Wavelet Based Numerical Method for Volterra Integro-Differential Equations on Unbounded Spatial Domains}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {3}, number = {4}, pages = {283--294}, abstract = {

The numerical solution of a parabolic Volterra integro-differential equation with a memory term on a one-dimensional unbounded spatial domain is considered. A quasi-wavelet based numerical method is proposed to handle the spatial discretisation, the Crank-Nicolson scheme is used for the time discretisation, and second-order quadrature to approximate the integral term. Some numerical examples are presented to illustrate the efficiency and accuracy of this approach.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.170813.131013a}, url = {http://global-sci.org/intro/article_detail/eajam/10858.html} }
TY - JOUR T1 - Crank-Nicolson Quasi-Wavelet Based Numerical Method for Volterra Integro-Differential Equations on Unbounded Spatial Domains AU - Man Luo, Da Xu & Limei Li JO - East Asian Journal on Applied Mathematics VL - 4 SP - 283 EP - 294 PY - 2018 DA - 2018/02 SN - 3 DO - http://doi.org/10.4208/eajam.170813.131013a UR - https://global-sci.org/intro/article_detail/eajam/10858.html KW - Parabolic Volterra integro-differential equation, unbounded spatial domain, quasi-wavelet, Crank-Nicolson method. AB -

The numerical solution of a parabolic Volterra integro-differential equation with a memory term on a one-dimensional unbounded spatial domain is considered. A quasi-wavelet based numerical method is proposed to handle the spatial discretisation, the Crank-Nicolson scheme is used for the time discretisation, and second-order quadrature to approximate the integral term. Some numerical examples are presented to illustrate the efficiency and accuracy of this approach.

Man Luo, Da Xu and Limei Li. (2018). Crank-Nicolson Quasi-Wavelet Based Numerical Method for Volterra Integro-Differential Equations on Unbounded Spatial Domains. East Asian Journal on Applied Mathematics. 3 (4). 283-294. doi:10.4208/eajam.170813.131013a
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