Solving Nonstiff Higher Order Odes Using Variable Order Step Size Backward Difference Directly

Ahmad Fadly Nurullah Rasedee, Mohamed bin Suleiman and Zarina Bibi Ibrahim

Mathematical Problems in Engineering, 2014, vol. 2014, 1-10

Abstract:

The current numerical techniques for solving a system of higher order ordinary differential equations (ODEs) directly calculate the integration coefficients at every step. Here, we propose a method to solve higher order ODEs directly by calculating the integration coefficients only once at the beginning of the integration and if required once more at the end. The formulae will be derived in terms of backward difference in a constant step size formulation. The method developed will be validated by solving some higher order ODEs directly using variable order step size. To simplify the evaluations of the integration coefficients, we find the relationship between various orders. The results presented confirmed our hypothesis.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:565137

DOI: 10.1155/2014/565137

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