scholarly journals The Initial Value Problem for Third and Fourth Order Dispersive Equations in One Space Dimension

2006 ◽  
Vol 49 (1) ◽  
pp. 1-38 ◽  
Author(s):  
Ryuichiro Mizuhara
Keyword(s):  
Fourth Order ◽  
Initial Value Problem ◽  
Space Dimension ◽  
Dispersive Equations ◽  
Initial Value ◽  
One Space Dimension

On solutions of the initial value problem for the nonlinear Schr�dinger equations in one space dimension

1986 ◽  
Vol 192 (4) ◽  
pp. 637-650 ◽  
Author(s):  
Nakao Hayashi ◽  
Kuniaki Nakamitsu ◽  
Masayoshi Tsutsumi
Keyword(s):  
Initial Value Problem ◽  
Space Dimension ◽  
Initial Value ◽  
One Space Dimension

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.

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