On the Runge Kutta Fixed Point Iterative Method of Soluition for the Blasius Boundary Value Problem of the Ordinary Differential Equation
Keywords:
Blasius problem, Runge Kutta method, Fixed point iterative method, Convergence
Abstract
In this paper, we consider the numerical solution of an ordinary differential equation problem with given boundary conditions. In approaching this we used the fixed point iterative method called the Runge Kutta method. This was exactly applied on the Blasius problem which model was formulated and solved iteratively using the FORTRAN programming language software that generated the solution in the last section of this work. The convergence of the solution was seen established.
References
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Young, M.T. (2009) "Runge Kutta Methods in the solution of Ordinary Differential Equations. Bulletin of the Brazilian Mathematical Society ol. 1(18-30)
Brice, Carnaha, Luther, H.A., Wikes, James O. (1969) "Applied Numerical methods." John Wesley and sons Inc. USA
Butcher, J.C. (1964) "Implicit Runge Kutta Processes," Math. Comp. 18.50-64
Butcher (2003) "The Numerical Analysis of Ordinary Differential Equations" John Willey and Sons New York, U.S.A.
Camara, S.K. (2005) "Analysis of different Runge Kutta Methods as applied to Boundary value problems of Ordinary Differential Equations" journal of computational methods Nol. 8 (54-71)
Collatz, L. (1960) "The Numerical Treatment of Differential Equations", Third Ed. Springer-Verlag, Berlin
Eziokwu, E.C. (2019) "Application of Runge Kutta iterative methods in the solution of ordinary differential equations" Osaka Journal of Mathematics Vol. 1(21-42)
Gear, C.W. (1965) "Hybrid Methods for initial Value Problems in Ordinary Differential Equations," Journal of the S.I.A.M 2 69-86
Hildebrand, F.B. (1956) "Introduction to Numerical Analysis", McGraw-Hill, New York
Ihiagwam P.C. (2001) "Abstract of the Nigerian Mathematical Society" Vol. 1(5-8)
Lapidus, L. (1962) "Digital Computation for Chemical Engineers," McGraw-Hill, New York
McCracken, D.D. and Dorn, W.S.(1964)"Numerical Methods and FORTRAN Programming",Wiley, NewYork
Milne,W.E and Reynolds, R.R. (1959) "Stability of a Numerical Solution of Differential Equations," Journal of the A.C.M. 6 196-203
Milne, W.E. (1953) "Numerical Solution of Differential Equations," Wiley, New York
Perry, J.H. (1950) "Chemical Engineers' Handbook," 3rd ed. McGraw-Hill, New York
Peter, R.T. (1994) "Numerical Analysis" PSTF
Young, M.T. (2009) "Runge Kutta Methods in the solution of Ordinary Differential Equations. Bulletin of the Brazilian Mathematical Society ol. 1(18-30)
Published
2019-07-02
How to Cite
Eziokwu, C. E., & Nkem , O. (2019). On the Runge Kutta Fixed Point Iterative Method of Soluition for the Blasius Boundary Value Problem of the Ordinary Differential Equation. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 2019(1), 483 - 495. Retrieved from http://ijmso.unilag.edu.ng/article/view/453
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