Abstract
In this paper, a matrix based method is considered for solving a class of 2DNVFIEs (Two Dimensional Nonlinear Volterra-Fredholm Integral Equations) of the second kind based on the operational Tau method. We developed this method with arbitrary polynomial bases (Standard, Legendre or Chebyshev polynomials) to obtain numerical solution of these equations. Some theoretical results are given to simplify and reduce the computation costs. In addition, L 2-convergence of the proposed method is proved when the given data are sufficiently smooth. Finally, some numerical examples are given to illustrate efficiency and accuracy of the proposed method.
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Hosseini, S.A., Shahmorad, S. & Talati, F. A matrix based method for two dimensional nonlinear Volterra-Fredholm integral equations. Numer Algor 68, 511–529 (2015). https://doi.org/10.1007/s11075-014-9858-4
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DOI: https://doi.org/10.1007/s11075-014-9858-4
Keywords
- Two dimensional nonlinear Volterra-Fredholm integral equation
- Matrix based method
- Operational Tau method