Numerical Solution of Functional Integral and Integro-Differential Equations by Using B-Splines

Affiliation(s)

Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.

Faculty of Education, Universiti Teknologi Malaysia, Johor, Malaysia.

Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.

Faculty of Education, Universiti Teknologi Malaysia, Johor, Malaysia.

ABSTRACT

This paper describes an approximating solution, based on Lagrange interpolation and spline functions, to treat functional integral equations of Fredholm type and Volterra type. This method extended to functional integral and integro-differential equations. For showing efficiency of the method we give some numerical examples.

This paper describes an approximating solution, based on Lagrange interpolation and spline functions, to treat functional integral equations of Fredholm type and Volterra type. This method extended to functional integral and integro-differential equations. For showing efficiency of the method we give some numerical examples.

Cite this paper

H. Gherjalar and H. Mohammadikia, "Numerical Solution of Functional Integral and Integro-Differential Equations by Using B-Splines,"*Applied Mathematics*, Vol. 3 No. 12, 2012, pp. 1940-1944. doi: 10.4236/am.2012.312265.

H. Gherjalar and H. Mohammadikia, "Numerical Solution of Functional Integral and Integro-Differential Equations by Using B-Splines,"

References

[1] H. Arndt, “Numerical Solution of Retarded Initial Value Problems: Local and Global Error and Step-Size Control,” Numerische Mathematik, Vol. 43, No. 3, 1984, pp. 343-360. doi:10.1007/BF01390178

[2] S. E. El-Gendi, “Chebyshev Solution of a Class of Functional Equations,” Computer Society of India, Vol. 8, 1971, pp. 271-307.

[3] M. Zennaro, “Natural Continuous Extension of RungeKutta Methods,” Mathematics of Computation, Vol. 46, No. 173, 1986, pp. 119-133. doi:10.1090/S0025-5718-1986-0815835-1

[4] L. Fox, D. F. Mayers, J. R. Ockendon and A. B. Taylor, “Ona Functional Differential Equation,” Journal of the Institute of Mathematics and Its Applications, Vol. 8, No. 3, 1971, pp. 271-307. doi:10.1093/imamat/8.3.271

[5] M. T. Rashed, “Numerical Solution of Functional Differential, Integral and Integro-Differential Equations,” Applied Mathematics and Computation, Vol. 156, No. 2, 2004, pp. 485-492. doi:10.1016/j.amc.2003.08.021

[6] K. Maleknejad and S. Rahbar, “Numerical Solution of Fredholm Integral Equations of the Second Kind by Using B-Spline Functions,” International Journal of Engineering Science, Vol. 11, No. 5, 2000, pp. 9-17.

[7] J. Stoer and R. Bulirsch, “Introduction to the Numerical Analysis,” Springer-Verlag, New York, 2002.

[8] L. L. Schumaker, “Spline Functions: Basic Theory,” John Wiley, New York, 1981.

[9] C. T. H. Baker, “The Numerical Solution of Integral Equations,” Clarendon Press, Oxford, 1969.

[10] K. Maleknejad and H. Derili, “Numerical Solution of Integral Equations by Using Combination of Spline-Collocation Method and Lagrange Interpolation,” Applied Mathematics and Computation, Vol. 175, No. 2, 2006, pp. 1235-1244.

[11] L. M. Delves and J. L. Mohammed, “Computational Methods For Integral Equations,” Cambridge University Press, Cambridge, 1985. doi:10.1017/CBO9780511569609

[12] M. T. Rashed, “An Expansion Method To Treat Integral Equations,” Applied Mathematics and Computation, Vol. 135, No. 2-3, 2003, pp. 73-79. doi:10.1016/S0096-3003(02)00347-8

[1] H. Arndt, “Numerical Solution of Retarded Initial Value Problems: Local and Global Error and Step-Size Control,” Numerische Mathematik, Vol. 43, No. 3, 1984, pp. 343-360. doi:10.1007/BF01390178

[2] S. E. El-Gendi, “Chebyshev Solution of a Class of Functional Equations,” Computer Society of India, Vol. 8, 1971, pp. 271-307.

[3] M. Zennaro, “Natural Continuous Extension of RungeKutta Methods,” Mathematics of Computation, Vol. 46, No. 173, 1986, pp. 119-133. doi:10.1090/S0025-5718-1986-0815835-1

[4] L. Fox, D. F. Mayers, J. R. Ockendon and A. B. Taylor, “Ona Functional Differential Equation,” Journal of the Institute of Mathematics and Its Applications, Vol. 8, No. 3, 1971, pp. 271-307. doi:10.1093/imamat/8.3.271

[5] M. T. Rashed, “Numerical Solution of Functional Differential, Integral and Integro-Differential Equations,” Applied Mathematics and Computation, Vol. 156, No. 2, 2004, pp. 485-492. doi:10.1016/j.amc.2003.08.021

[6] K. Maleknejad and S. Rahbar, “Numerical Solution of Fredholm Integral Equations of the Second Kind by Using B-Spline Functions,” International Journal of Engineering Science, Vol. 11, No. 5, 2000, pp. 9-17.

[7] J. Stoer and R. Bulirsch, “Introduction to the Numerical Analysis,” Springer-Verlag, New York, 2002.

[8] L. L. Schumaker, “Spline Functions: Basic Theory,” John Wiley, New York, 1981.

[9] C. T. H. Baker, “The Numerical Solution of Integral Equations,” Clarendon Press, Oxford, 1969.

[10] K. Maleknejad and H. Derili, “Numerical Solution of Integral Equations by Using Combination of Spline-Collocation Method and Lagrange Interpolation,” Applied Mathematics and Computation, Vol. 175, No. 2, 2006, pp. 1235-1244.

[11] L. M. Delves and J. L. Mohammed, “Computational Methods For Integral Equations,” Cambridge University Press, Cambridge, 1985. doi:10.1017/CBO9780511569609

[12] M. T. Rashed, “An Expansion Method To Treat Integral Equations,” Applied Mathematics and Computation, Vol. 135, No. 2-3, 2003, pp. 73-79. doi:10.1016/S0096-3003(02)00347-8