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Exponential Spline Approximation for the Solution of Third-Order Boundary Value Problems

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Data Management, Analytics and Innovation

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 808))

Abstract

A general third-order boundary value problems (BVPs) are considered here, to find the approximate solution. An exponential amalgamation of cubic spline functions is used to form a novel numerical approach. Finite difference method supports the developed system to solve the problems slickly. Our method is convergent and second-order accurate. Numerical examples show that the method congregates with sufficient accuracy to the exact solutions.

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References

  1. Said, E. A. (2001). Numerical solutions for system of third-order boundary value problems. International Journal of Computer Mathematics, 78, 111–121.

    Article  MathSciNet  Google Scholar 

  2. Noor, M. A., & Said, E. A. (2002). Finite-difference method for a system of third-order boundary-value problems. Journal of Optimization Theory and Applications, 112, 627–637.

    Article  MathSciNet  Google Scholar 

  3. Salama, A. A., & Mansour, A. A. (2005). Fourth-order finite-difference method for third-order boundary-value problems. Numerical Heat Transfer, Part B: Fundamentals, An International Journal of Computation and Methodology, 47, 383–401.

    Article  Google Scholar 

  4. Noor, M. A., Said, E. A., & Noor, K. I. (2012). Finite difference method for solving a system of third-order boundary value problems. Journal of Applied Mathematics, 2012, 1–10.

    MathSciNet  MATH  Google Scholar 

  5. Said, E. A., & Noor, M. A. (2003). Cubic splines method for a system of third-order boundary value problems. Applied Mathematics and Computation, 142, 195–204.

    Article  MathSciNet  Google Scholar 

  6. Said, E. A. (2008). A cubic spline method for solving a system of third order boundary value problems. International Journal of Pure and Applied Mathematics, 43, 677–686.

    MathSciNet  Google Scholar 

  7. Noor, M. A., & Said, E. A. (2004). Quartic splines solutions of third-order obstacle problems. Applied Mathematics and Computation, 153, 307–316.

    Article  MathSciNet  Google Scholar 

  8. Khan, A., & Aziz, T. (2003). The numerical solution of third-order boundary-value problems using quintic splines. Applied Mathematics and Computation, 137, 253–260.

    Article  MathSciNet  Google Scholar 

  9. Islam, S. U., Khan, M. A., Tirmizi, I. A., & Twizell, E. H. (2005). Non-polynomial splines approach to the solution of a system of third-order boundary-value problems. Applied Mathematics and Computation, 168, 152–163.

    Article  MathSciNet  Google Scholar 

  10. Islam, S. U., Tirmizi, I. A., & Khan, M. A. (2007). Quartic non-polynomial spline approach to the solution of a system of third order boundary value problems. Journal of Mathematical Analysis and Applications, 335, 1095–1104.

    Article  MathSciNet  Google Scholar 

  11. Talaat, S., & Danaf, E. (2008). Quartic non-polynomial spline solutions for third order two-point boundary value problem. International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, 2, 637–640.

    Google Scholar 

  12. Khan, A., & Sultana, T. (2012). Non-polynomial quintic spline solution for the system of third order boundary value problems. Numerical Algorithms, 59, 541–559.

    Article  MathSciNet  Google Scholar 

  13. Srivastava, P. K., & Kumar, M. (2012). Numerical algorithm based on quintic non-polynomial spline for solving third-order boundary value problems associated with draining and coating flow. Chinese Annals of Mathematics, 33, 831–840.

    Article  MathSciNet  Google Scholar 

  14. Li, L., & Gao, J. (2014). Non-polynomial spline method for a system of third order obstacle boundary value problems. Journal of Mathematical Sciences, Advances and Applications, 30, 49–69.

    Google Scholar 

  15. Salam, F. A. A. E., Sabbagh, A. A. E., & Zaki, Z. A. (2010). The numerical solution of linear third order boundary value problems using non-polynomial spline technique. Journal of American Science, 6, 303–309.

    Google Scholar 

  16. Pandey, P. K. (2017). A numerical method for the solution of general third order boundary value problem in ordinary differential equations. Bulletin of the International Mathematical Virtual Institute, 7, 129–138.

    MathSciNet  Google Scholar 

  17. Said, E. A. (2004). Computational techniques for system of third order boundary value problems. Journal of Nonlinear Functional Analysis and Applications, 9, 305–314.

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Birla Institute of Technology, Allahabad, 211000, Uttar Pradesh, India

    Anju Chaurasia

  2. Department of Mathematics, Birla Institute of Technology, Allahabad, 211000, Uttar Pradesh, India

    Prakash Chandra Srivastava

  3. Department of Mathematics, Jaypee Institute of Information Technology, Noida, 201307, Uttar Pradesh, India

    Yogesh Gupta

Authors
  1. Anju Chaurasia
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  2. Prakash Chandra Srivastava
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  3. Yogesh Gupta
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Corresponding author

Correspondence to Anju Chaurasia .

Editor information

Editors and Affiliations

  1. Department of Automatics and Applied Software, Aurel Vlaicu University of Arad, Arad, Romania

    Valentina Emilia Balas

  2. Audyogik Tantra Shikshan Sanstha’s, IICMR, Pune, Maharashtra, India

    Neha Sharma

  3. Faculty of Engineering and Technology, A. K. Choudhury School of Information Technology, Kolkata, West Bengal, India

    Amlan Chakrabarti

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© 2019 Springer Nature Singapore Pte Ltd.

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Chaurasia, A., Srivastava, P.C., Gupta, Y. (2019). Exponential Spline Approximation for the Solution of Third-Order Boundary Value Problems. In: Balas, V., Sharma, N., Chakrabarti, A. (eds) Data Management, Analytics and Innovation. Advances in Intelligent Systems and Computing, vol 808. Springer, Singapore. https://doi.org/10.1007/978-981-13-1402-5_26

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  • DOI: https://doi.org/10.1007/978-981-13-1402-5_26

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-1401-8

  • Online ISBN: 978-981-13-1402-5

  • eBook Packages: EngineeringEngineering (R0)

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