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Solution of Higher-Order ODEs Using Backward Difference Method

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Listed:
  • Mohamed Bin Suleiman
  • Zarina Bibi Binti Ibrahim
  • Ahmad Fadly Nurullah Bin Rasedee

Abstract

The current numerical technique for solving a system of higher-order ordinary differential equations (ODEs) is to reduce it to a system of first-order equations then solving it using first-order ODE methods. Here, we propose a method to solve higher-order ODEs directly. The formulae will be derived in terms of backward difference in a constant stepsize formulation. The method developed will be validated by solving some higher-order ODEs directly with constant stepsize. To simplify the evaluations of the integration coefficients, we find the relationship between various orders. The result presented confirmed our hypothesis.

Suggested Citation

  • Mohamed Bin Suleiman & Zarina Bibi Binti Ibrahim & Ahmad Fadly Nurullah Bin Rasedee, 2011. "Solution of Higher-Order ODEs Using Backward Difference Method," Mathematical Problems in Engineering, Hindawi, vol. 2011, pages 1-18, July.
    • Handle: RePEc:hin:jnlmpe:810324
    DOI: 10.1155/2011/810324
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