TL;DR
This paper reviews a recent Runge-Kutta type method for solving fourth-order ordinary differential equations and benchmarks its performance against the classical RK4 method.
Contribution
It summarizes a new RKFD method for fourth-order ODEs and provides an independent implementation and comparison with RK4.
Findings
The RKFD method is effective for fourth-order ODEs.
Benchmark results show performance differences between RKFD and RK4.
The review clarifies the advantages of the RKFD approach.
Abstract
In this paper, a recently published method [Hussain, Ismail, Senua, Solving directly special fourth-order ordinary differential equations using Runge-Kutta type method, J. Comput. Appl. Math. 306 (2016) 179-199] for solving fourth-order ordinary differential equations is summarized and reviewed. An independant implementation of one of the published methods is also tested and benchmarked against the RK4 method.
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Taxonomy
TopicsNumerical methods for differential equations · Fractional Differential Equations Solutions · Differential Equations and Numerical Methods