Solving Systems of Volterra Integral Equations with Cardinal Splines

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References

[1] Liu, X. and Xie, J. (2014) Numerical Methods for Solving Systems of Fredholm Integral Equations with Cardinal Splines. AIP Conference Proceedings, 1637, 590.

http://dx.doi.org/10.1063/1.4904628

[2] Adawi, A. and Awawdeh, F. (2009) A Numerical Method for Solving Linear Integral Equations. International Journal of Contemporary Mathematical Sciences, 4, 485-496.

[3] Polyanin, A.D. (1998) Handbook of Integral Equations. CRC Press LLC, Boca Raton.

http://dx.doi.org/10.1201/9781420050066

[4] Saeed, R.K. and Ahmed, C.S. (2008) Approximate Solution for the System of Non-Linear Volterra Integral Equations of the Second Kind by Using Block-by-block Method. Australian Journal of Basic and Applied Sciences, 2, 114-124.

[5] Schoenberg, I.J. (1964) On Trigonometric Spline Functions. Journal of Mathematics and Mechanics, 13, 795-825.

[6] Chui, C.K. (1988) Multivariate Splines. SIAM, Philadelphia.

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[7] Liu, X. (2001) Bivariate Cardinal Spline Functions for Digital Signal Processing. In: Kopotum, K., Lyche, T. and Neamtu, M., Eds., Trends in Approximation Theory, Vanderbilt University, Nashville, 261-271.

[8] Liu, X. (2007) Interpolation by Cardinal Exponential Splines. The Journal of Information and Computational Science, 4, 179-194.

[9] Liu, X. (2013) The Applications of Orthonormal and Cardinal Splines in Solving Linear Integral Equations. In: Akis, V., Ed., Essays on Mathematics and Statistics, V4, Athens Institute for Education and Research, 41-58.

[10] Liu, X., Xie, J. and Xu, L. (2014) The Applications of Cardinal Trigonometric Splines in Solving Nonlinear Integral Equations. Applied Mathematics, 2014, Article ID: 213909.

[11] Liu, X. (2006) Univariate and Bivariate Orthornormal Splines and Cardinal Splines on the Compact Supports. Journal of Computational and Applied Mathematics, 195, 93-105.

http://dx.doi.org/10.1016/j.cam.2005.04.070