Numerical Solution of Volterra Integral Equation and its Error Estimates Via Spectral Method

Authors

  • Olagunju Adeyemi S. Department of Mathematics, Federal University Lafia, 950101, Nigeria
  • Oladotun Matthew Ogunlaran Department of Mathematics and Statistics, Bowen University Iwo, 232101, Nigeria
  • Ibrahim Adebisi A. Department of Mathematical Sciences, Oduduwa University Ipetumodu, 220371, Nigeria

Keywords:

Spectral method, Chebyshev basis function, Coefficients, Volterra Integral equations, Error estimates.

Abstract

In this article, numerical solution of Volterra integral equations is considered. A new approach in the application of spectral method is proposed, wherein Chebyshev polynomial of the first kind  serves as the basis function. Essentially, the method is based on the approach of series solution where coefficients of  in the residual equations are correspondingly equated to yield system of equations. Expression for error estimates which effectively serves as upper bound for accrued errors is arrived at. To illustrate the accuracy and effectiveness of the method and its error estimates, numerical examples on some standard integral equations are given.

References

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[9] A. M. Wazwaz. Linear and Nonlinear Integral equations, methods and application. Beijing: Higher Education Press, and Berlin Heidelbeerg: Springer-verlag, 2011.
[10] L. N. Trefethen. Spectral Methods in MATLAB. Philadelphia: SIAM, 2000.

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Published

2017-04-08

How to Cite

Adeyemi S., O., Ogunlaran, O. M., & Adebisi A., I. (2017). Numerical Solution of Volterra Integral Equation and its Error Estimates Via Spectral Method. American Academic Scientific Research Journal for Engineering, Technology, and Sciences, 30(1), 47–56. Retrieved from https://asrjetsjournal.org/index.php/American_Scientific_Journal/article/view/2507

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