A NEW INTEGRATOR FOR SPECIAL THIRD ORDER DIFFERENTIAL EQUATIONS WITH APPLICATION TO THIN FILM FLOW PROBLEM

作者：Jikantoro Y D^*; Ismail F; Senu N; Ibrahim Z B

来源：Indian Journal of Pure and Applied Mathematics, 2018, 49(1): 151-167.

DOI：10.1007/s13226-018-0259-6

• Hybrid method
• three-step method
• Taylor series
• order conditions
• third order ordinary differential equations
• numerical integrator

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.

• 出版日期2018-3