A New Integrator for Special Third Order Differential Equations With Application to Thin Film Flow Problem

Y. D. Jikantoro (), F. Ismail, N. Senu and Z. B. Ibrahim
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Y. D. Jikantoro: University Putra Malaysia
F. Ismail: University Putra Malaysia
N. Senu: University Putra Malaysia
Z. B. Ibrahim: University Putra Malaysia

Indian Journal of Pure and Applied Mathematics, 2018, vol. 49, issue 1, 151-167

Abstract: Abstract In recent time, Runge-Kutta methods that integrate special third order ordinary differential equations (ODEs) directly are proposed to address efficiency issues associated with classical Runge-Kutta methods. Albeit, the methods require evaluation of three set of equations to proceed with the numerical integration. In this paper, we propose a class of multistep-like Runge-Kutta methods (hybrid methods), which integrates special third order ODEs directly. The method is completely derivative-free. Algebraic order conditions of the method are derived. Using the order conditions, a four-stage method is presented. Numerical experiment is conducted on some test problems. The method is also applied to a practical problem in Physics and engineering to ascertain its validity. Results from the experiment show that the new method is more accurate and efficient than the classical Runge-Kutta methods and a class of direct Runge-Kutta methods recently designed for special third order ODEs.

Keywords: Hybrid method; three-step method; Taylor series; order conditions; third order ordinary differential equations; numerical integrator (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s13226-018-0259-6

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