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Lucas Polynomial Approach for System of High-Order Linear Differential Equations and Residual Error Estimation

Author

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  • Muhammed Çetin
  • Mehmet Sezer
  • Coşkun Güler

Abstract

An approximation method based on Lucas polynomials is presented for the solution of the system of high-order linear differential equations with variable coefficients under the mixed conditions. This method transforms the system of ordinary differential equations (ODEs) to the linear algebraic equations system by expanding the approximate solutions in terms of the Lucas polynomials with unknown coefficients and by using the matrix operations and collocation points. In addition, the error analysis based on residual function is developed for present method. To demonstrate the efficiency and accuracy of the method, numerical examples are given with the help of computer programmes written in Maple and Matlab .

Suggested Citation

  • Muhammed Çetin & Mehmet Sezer & Coşkun Güler, 2015. "Lucas Polynomial Approach for System of High-Order Linear Differential Equations and Residual Error Estimation," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-14, February.
    • Handle: RePEc:hin:jnlmpe:625984
    DOI: 10.1155/2015/625984
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    Cited by:

    1. Singh, P.K. & Saha Ray, S., 2023. "An efficient numerical method based on Lucas polynomials to solve multi-dimensional stochastic Itô-Volterra integral equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 826-845.

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