Fourth order singularly perturbed boundary value problems via initial value techniques

2014 ◽  
Vol 8 ◽  
pp. 619-632 ◽  
Author(s):  
Hradyesh Kumar Mishra ◽  
Sonali Saini
Keyword(s):  
Boundary Value Problems ◽  
Fourth Order ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
Initial Value

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

2021 ◽  
Vol 3 (1) ◽  
pp. 8-21 ◽  
Author(s):  
Mst. Sharmin Banu ◽  
Keyword(s):  
Boundary Value Problems ◽  
Fourth Order ◽  
Boundary Value ◽  
Exact Result ◽  
Sixth Order ◽  
Initial Value ◽  
Step Size ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Fourth Order Method

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.

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