A Comparative Study on Numerical Solution of Initial Value Problem by Using Euler�s Method, Modified Euler�s Method and Runge-Kutta Method

2018 ◽  
Vol 9 (5) ◽  
pp. 493-500
Author(s):  
Md. Kamruzzaman ◽  
Mithun Chandra Nath
Keyword(s):  
Comparative Study ◽  
Numerical Solution ◽  
Initial Value Problem ◽  
Kutta Method ◽  
Initial Value ◽  
Runge Kutta Method ◽  
Runge Kutta

A New Efficient Ode Solver For Solving Initial Value Problem

1998 ◽  
pp. 47-56
Author(s):  
Nazeeruddin Yaacob ◽  
Bahrom Sanugi
Keyword(s):  
Stability Analysis ◽  
Explicit Formula ◽  
Fourth Order ◽  
Initial Value Problem ◽  
Harmonic Mean ◽  
Kutta Method ◽  
Initial Value ◽  
Order Accuracy ◽  
Runge Kutta Method ◽  
Runge Kutta

In this paper we develop a new three-stage,fourth order explicit formula of Runge-Kutta type based on Arithmetic and Harmonic means.The error and stability analyses of this method indicate that the method is stable and efficient for nonstiff problems.Two examples are given which illustrate the fcurth order accuracy of the method. Keywords: Runge-Kutta method, Harmonic Mean, three-stage, fourth-order, covergence and stability analysis.

THREE POINTS BLOCK EMBEDDED DIAGONALLY IMPLICIT RUNGE-KUTTA METHOD FOR SOLVING ODES

2021 ◽  
Vol 10 (11) ◽  
pp. 3449-3460
Author(s):  
Y.F. Rahim ◽  
M.E.H. Hafidzuddin
Keyword(s):  
Initial Value Problem ◽  
Numerical Results ◽  
Kutta Method ◽  
Initial Value ◽  
Stiff System ◽  
The Third ◽  
Runge Kutta Method ◽  
One Step ◽  
Runge Kutta

Block Embedded Diagonally Implicit Runge-Kutta (BEDIRK4(3)) me- thod derived using Butcher analysis and equi-distribution of error approach is outperformed standard Runge-Kutta (RK) formulae. BEDIRK4(3) method produces approximation to the solution of initial value problem (IVP) at a block of three points simultaneously. The standard one step RK3(2) method is used to approximate the solution at the first point of the block. At the second points the solution is approximated using RK4(2) method which is generated by the previous research. The same approach is used to obtain the solution at the third point. The code for this method was built and the algorithm developed is suitable for solving stiff system. The efficiency of the method is supported by some numerical results.

scholarly journals Eficiencia y efectividad del método de continuación aplicado al diseño biaxial de columnas cortas de concreto reforzado

Respuestas ◽  
2013 ◽  
Vol 18 (2) ◽  
pp. 6-15
Author(s):  
Álvaro Ortega-Sierra ◽  
Breiner Reynaldo Sierra-Santos
Keyword(s):  
Initial Value Problem ◽  
Continuation Method ◽  
Kutta Method ◽  
Biaxial Bending ◽  
Initial Value ◽  
Step Size ◽  
Runge Kutta Method ◽  
Quasi Experimental ◽  
Runge Kutta ◽  
The One

 La investigación se realizó con 178 diseños correspondientes a columnas de sección cuadrada, por medio de un estudio descriptivo y cuasi experimental. Para dar solución al sistema de tres ecuaciones no lineales que gobierna el diseño se aplicó el Método de Continuación. De acuerdo con éste método, una solución equivalente a la del sistema anterior está dada por la que se obtiene cuando t=1 en un problema de valor inicial en el intervalo 0 ≤ t ≤ 1, el cual fue resuelto implementando el método de Runge-Kutta de orden 4 con diferentes tamaños de paso. Para explorar la eficiencia se investigó acerca de la existencia de diferencias significativas entre promedios del error numérico al final de dos iteraciones consecutivas, considerando un máximo de cinco. Respecto a la efectividad, ésta se cuantificó para diferentes tolerancias del error en función del tamaño de paso y del número de iteraciones.Palabras clave: flexión biaxial, eficiencia, efectividad, problema de valor inicial, Método de Runge-Kutta, tamaño de paso, iteración. ABSTRACTThe research was conducted with 178 designs for square columns, using a quasi-experimental descriptive study. To solve the system of three nonlinear equations that govern the design was applied continuation method. According to this method, an equivalent solution to the above system is given by the one obtained when an initial value problem in the interval 0 d t d 1, which was resolved by implementing the Runge-Kutta method of order 4 with different sizes step. To explore the efficiency was investigated on the existence of significant differences between means of numerical error at the end of two consecutive iterations, considering a maximum of five. With regard to effectiveness, this was quantified for different tolerances of the error depending on the step size and number of iterations.Keywords: biaxial bending, efficiency, effectiveness, initial value problem, Runge-Kutta method, step size, iteration.  

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