Fourth Derivative Methods for Solving Fourth-Order Initial Value Problems Using an Optimized Three-Step, Two-Off Grid

Raymond, Dominic, Donald John Zirra, Nuhu Bata Malgwi

doi:https://doi.org/10.59232/MS-V3I2P102

Research Article | Open Access | Download Full Text

Volume 3 | Issue 2 | Year 2025 | Article Id: MS-V3I2P102 DOI: https://doi.org/10.59232/MS-V3I2P102

Fourth Derivative Methods for Solving Fourth-Order Initial Value Problems Using an Optimized Three-Step, Two-Off Grid

Raymond, Dominic, Donald John Zirra, Nuhu Bata Malgwi

Received	Revised	Accepted	Published
07 Feb 2025	09 Mar 2025	05 Apr 2025	30 Apr 2025

Citation

Raymond, Dominic, Donald John Zirra, Nuhu Bata Malgwi. “Fourth Derivative Methods for Solving Fourth-Order Initial Value Problems Using an Optimized Three-Step, Two-Off Grid.” DS Journal of Modeling and Simulation, vol. 3, no. 2, pp. 10-21, 2025.

Abstract

In order to solve fourth-order ordinary differential equations, this article presents an optimized three-step, two-off-grid hybrid point fourth derivative method. The method uses an exponential function as the basis function for a chosen three hybrid points, appropriately optimizing one of the two off-grid points by setting the principal term of the local truncation error to zero and using the local truncation error to determine the approximate values of the unknown parameter. The method’s basic properties were examined, and the developed method was applied to work out some fourth order initial value problems of ordinary differential equations. Based on the numerical results, it is observed that our new approach provides a better approximation than the existing method when compared to our result.

Keywords

Optimize off-grid, Local truncation error, Free-parameter, Three-step, Fourth derivative.

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