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.
Publisher
Universe Publishing Group - UniversePG
Reference38 articles.
1. Ababneh, O.Y., Ahmad, R. and Ismail, E.S. (2009). New multi-step Runge-Kutta method. Appl. Mathematical Sciences, 3(45), 2255-2262.
2. http://www.m-hikari.com/ams/ams-password-2009/ ams-password45-48-2009/ababnehAMS45-48-200 9-2.pdf
3. Ademiluyi, R.A., Babatola, P.O. and Kayode, S.J. (2001). Semi implicit Rational Runge-Kutta formulas of approximation of stiff initial value problems in ODEs. Journal of Mathematical Science and Education, 3, pp.1-25.
4. Agam, S.A. and Yahaya, Y.A. (2014). A highly efficient implicit Runge-Kutta method for first order ordinary differential equations. African j. of mathematics and Computer Science Research, 7(5), pp.55-60. https://academicjournals.org/journal/AJMCSR/article-abstract/9D7ECC646284
5. Ahmed M, and Iqbal MA. (2020). An execution of a mathematical example using Euler’s Phi-function in Hill Chiper cryptosystem, Int. J. Mat. Math. Sci., 2(6), 99-103.