Semiorthogonal B-spline Wavelet for Solving 2D- Nonlinear Fredholm-Hammerstein Integral Equations

Authors

  • Eman Ali Hussain College of Science, University of AL- Mustansiriyah, Iraq
  • Lamyaa H. Ali College of Science, University of ALMustansiriyah, Iraq

DOI:

https://doi.org/10.24297/jam.v6i1.3638

Keywords:

wavelet, spline, integral equation, Fredholm-Hammerstein.

Abstract

This work is concerned with the study of the second order (linear) semiorthogonal B-spline wavelet method to solve one-dimensional nonlinear Fredholm-Hammerstein integral equations of the second kind. Proof of the existence and uniqueness solution for the two-dimensional Fredholm-Hammerstein nonlinear integral equations of the second kind was introduced. Moreover, generalization the second order (linear) semiorthogonal B-spline wavelet method was achieved and then using it to solve two-dimensional nonlinear Fredholm-Hammerstein integral equations of the second kind. This method transform the one-dimensional and two-dimensional nonlinear Fredholm-Hammerstein integral equations of the second kind to a system of algebraic equations by expanding the unknown function as second order (linear) semiorthogonal B-spline wavelet with unknown coefficients. The properties of these wavelets functions are then utilized to evaluate the unknown coefficients. Also some of illustrative examples which show that the second order (linear) semiorthogonalB-spline wavelet method give good agreement with the exact solutions.

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Author Biographies

Eman Ali Hussain, College of Science, University of AL- Mustansiriyah, Iraq

Asst. Prof, Dr., Department of Mathematics

Lamyaa H. Ali, College of Science, University of ALMustansiriyah, Iraq

Asst. Lec., Department of Mathematics

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Published

2014-01-30

How to Cite

Hussain, E. A., & Ali, L. H. (2014). Semiorthogonal B-spline Wavelet for Solving 2D- Nonlinear Fredholm-Hammerstein Integral Equations. JOURNAL OF ADVANCES IN MATHEMATICS, 6(1), 876–888. https://doi.org/10.24297/jam.v6i1.3638

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Articles