Numerical Solution of Freholm-Volterra Integral Equations by Using Scaling Function Interpolation Method

ABSTRACT

Wavelet methods are a very useful tool in solving integral equations. Both scaling functions and wavelet functions are the key elements of wavelet methods. In this article, we use scaling function interpolation method to solve Volterra integral equations of the first kind, and Fredholm-Volterra integral equations. Moreover, we prove convergence theorem for the numerical solution of Volterra integral equations and Freholm-Volterra integral equations. We also present three examples of solving Volterra integral equation and one example of solving Fredholm-Volterra integral equation. Comparisons of the results with other methods are included in the examples.

Cite this paper

Y. Al-Jarrah and E. Lin, "Numerical Solution of Freholm-Volterra Integral Equations by Using Scaling Function Interpolation Method,"*Applied Mathematics*, Vol. 4 No. 1, 2013, pp. 204-209. doi: 10.4236/am.2013.41A031.

Y. Al-Jarrah and E. Lin, "Numerical Solution of Freholm-Volterra Integral Equations by Using Scaling Function Interpolation Method,"

References

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[5] A. S. Shamloo, S. Shaker and A. Madadi, “Numerical Solution of Fredholm-Volterra Integral Equation by the Sunc Function,” American Journal Computation Mathematics, Vol. 2, No. 2, 2012, pp. 136-142. doi:10.4236/ajcm.2012.22019

[1] E. B. Lin and N. Liu, “Legendre Wavelet Method for Numerical Solutions of Partial Differential Equations,” Numerical Methods of Partial Differential Equation, Vol. 26, No. 1, 2010, pp. 81-94. doi:10.1002/num.20417

[2] C. K. Chui, “In Introduction to Wavelets,” Academic Press, Boston, 1992.

[3] E, B. Lin and X. Zhou, “Coiflet Interpolation and Approximate Solutions of Elliptic Partial Differential Equations,” Methods for Partial Differential Equations, Vol. 13, No. 4, 1997, pp. 302-320.

[4] M. T. Rashad, “Numerical Solution of the Integral Equations of the First Kind,” Applied Mathematics and Computation, Vol. 145, No. 2-3, 2003, pp. 413-420. doi:10.1016/S0096-3003(02)00497-6

[5] A. S. Shamloo, S. Shaker and A. Madadi, “Numerical Solution of Fredholm-Volterra Integral Equation by the Sunc Function,” American Journal Computation Mathematics, Vol. 2, No. 2, 2012, pp. 136-142. doi:10.4236/ajcm.2012.22019