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A Comparative Study on Classical Fourth Order and Butcher Sixth Order Runge-Kutta Methods with Initial and Boundary Value Problems


Mst. Sharmin Banu1*, Irfan Raju2, and Samiran Mondal1


1Department of Mathematics, Jashore University of Science and Technology, Jashore, Bangladesh; and 2Department of Arts and Sciences, Bangladesh Army University of Science and Technology, Saidpur, Bangladesh.

*Correspondence: msbsharmin_math@just.edu.bd (Mst. Sharmin Banu, Lecturer, Department of Mathematics, Jashore University of Science and Technology, Jashore, Bangladesh).

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ABSTRACT

In this paper, it is discussed about Runge-Kutta fourth-order method and Butcher Sixth order Runge-Kutta method for approximating a numerical solution of higher-order initial value and boundary value ordinary differential equations. The proposed methods are most efficient and extolled practically for solving these problems arising indifferent sector of science and engineering. Also, the shooting method is applied to convert the boundary value problems to initial value problems. Illustrative examples are provided to verify the accuracy of the numerical outcome and compared the approximated result with the exact result. The approximated results are found in good agreement with the result of the exact solution and firstly converge to more accuracy in the solution when step size is very small. Finally, the error with different step sizes is analyzed and compared to these two methods. 


Keywords: Runge-Kutta fourth order method, Shooting method, Initial value, and boundary value problem.


Citation: Banu MS, Raju I, and Mondal S. (2021). A comparative study on classical fourth order and butcher sixth order Runge-Kutta methods with initial and boundary value problems, Int. J. Mat. Math. Sci., 3(1), 8-21. 

https://doi.org/10.34104/ijmms.021.08021


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