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A finite difference method for the numerical solving general third order boundary-value problem with an internal boundary condition

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Abstract

In this paper we have proposed a finite difference method for the numerical solving general third order boundary-value problem. Under appropriate conditions we have discussed the convergence of the proposed method. The computational results in experiment on test problems verify the efficiency and theoretically established second order accuracy of the proposed method.

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References

  1. Gregus, M. Third Order Linear Differential Equations,Mathematics and its Applications (East European Series) (D. Reidel Publishing Company, Dordrecht–Boston–Lancaster–Tokyo 1987).

    Book  Google Scholar 

  2. Jackson, L. “Existence and Uniqueness of Solutions of Boundary-Value Problems for ThirdOrderDifferential Equations”, J.Diff. Eqs. 13, 432–437 (1973).

    Article  MATH  Google Scholar 

  3. Gupta, C. P. and Lakshmikantham, V. “Existence and Uniqueness Theorems for a Third-Order Three Point Boundary-Value Problem”, Nonlinear Analysis: Theory, Methods & Applications 16, No. 11, 949–957 (1991).

    Article  MathSciNet  MATH  Google Scholar 

  4. Murty, K. N. and Rao Y. S. “A Theory for Existence and Uniqueness of Solutions to Three-Point Boundary- Value Problems”, J.Math. Anal. and Appl. 167, No. 1, 43–48 (1992).

    Article  MathSciNet  MATH  Google Scholar 

  5. Henderson, J. and Prasad, K. R. “Existence and Uniqueness of Solutions of Three-Point Boundary-Value Problems on Time Scales”, Nonlin. Studies 8, 1–12 (2001).

    MATH  Google Scholar 

  6. Gregus, M. and Abdel Karim, R. I. I. “Boundedness of the Solutions of the Differential Equation (py')”+(py')' + ry = 0”, Proc. Math. and Phys. Soc., U. A. R. 32, 107–110 (1968).

    MathSciNet  MATH  Google Scholar 

  7. Agarwal, R. P. Boundary-Value Problems for Higher Order Differential Equations (World Scientific, Singapore, 1986).

    Book  MATH  Google Scholar 

  8. Na, T. Y. Computational Methods in Engineering Boundary-Value Problems (Academic Press, New York, 1979).

    MATH  Google Scholar 

  9. Al-Said, E. A. “Numerical Solutions for System of Third-Order Boundary-Value Problems”, International Journal of ComputerMathematics 78, No. 1, 111–121 (2001).

    Article  MathSciNet  MATH  Google Scholar 

  10. Khan, A. and Aziz, T. “The Numerical Solution of Third-Order Boundary-Value Problems Using Quintic Splines”, AppliedMathematics and Computation 137, No. 2–3, 253–260 (2003).

    MathSciNet  MATH  Google Scholar 

  11. Islam, S., Khan, M. A., Tirmizi, I. A. and Twizell, E. H. “Non-Polynomial Splines Approach to the Solution of a System of Third-Order Boundary-Value Problems”, AppliedMathematics and Computation 168, No. 1, 152–163 (2005).

    MathSciNet  MATH  Google Scholar 

  12. Li, X. and Wu, B. “Reproducing Kernel Method for Singular Multi-Point Boundary-Value Problems”, Mathematical Sciences 6 (16), Article ID doi:10.1186/2251-7456-6-16 (2012).

    Google Scholar 

  13. Pandey, P. K. “The Numerical Solution of Third Order Differential Equation Containing the First Derivative”, Neural Parallel & Scientific Comp. 13, 297–304 (2005).

    MathSciNet  MATH  Google Scholar 

  14. Varga, R. S. Matrix Iterative Analysis, Second Revised and Expanded Edition (Springer-Verlag, Heidelberg, 2000).

    Book  Google Scholar 

  15. Horn, R. A. and Johnson, C. R. Matrix Analysis (Cambridge University Press, New York, NY 10011, USA, 1990).

    MATH  Google Scholar 

  16. Jator, S. N. “On the Numerical Integration of Third Order Boundary-Value Problems by a Linear Multistep Method”, International Journal of Pure and AppliedMathematics 46, No. 3, 375–388 (2008).

    MathSciNet  MATH  Google Scholar 

  17. Krajcinovic D. “Sandwich Beam Analysis”, Journal of AppliedMechanics, 773–778 (1971).

    Google Scholar 

  18. Ghazala, A., Muhammad, T., Shahid, S. S. and Hamood, U. R. “Solution of a Linear Third Order Multi- Point Boundary Value ProblemUsing RKM”, British Journal ofMathematics & Computer Science 3, No. 2, 180–194 (2013).

    Google Scholar 

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Authors and Affiliations

  1. Dyal Singh College (University of Delhi), Lodhi Road, New Delhi, 110003, India

    P. K. Pandey

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  1. P. K. Pandey
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Correspondence to P. K. Pandey.

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The text was submitted by the author in English.

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Pandey, P.K. A finite difference method for the numerical solving general third order boundary-value problem with an internal boundary condition. Russ Math. 61, 29–38 (2017). https://doi.org/10.3103/S1066369X17120040

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  • DOI: https://doi.org/10.3103/S1066369X17120040

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