Numerical Simulations of a Polydisperse Sedimentation Model by Using Spectral WENO Method with Adaptive Multiresolution

2016 ◽  
Vol 13 (06) ◽  
pp. 1650037
Author(s):  
Carlos A. Vega ◽  
Francisco Arias
Keyword(s):  
Convergence Rates ◽  
Time Discretization ◽  
Strong Stability ◽  
Kutta Method ◽  
Strong Stability Preserving ◽  
Third Order ◽  
Runge Kutta Method ◽  
Sedimentation Model ◽  
Runge Kutta ◽  
Fifth Order

In this work, we apply adaptive multiresolution (Harten’s approach) characteristic-wise fifth-order Weighted Essentially Non-Oscillatory (WENO) for computing the numerical solution of a polydisperse sedimentation model, namely, the Höfler and Schwarzer model. In comparison to other related works, time discretization is carried out with the ten-stage fourth-order strong stability preserving Runge–Kutta method which is more efficient than the widely used optimal third-order TVD Runge–Kutta method. Numerical results with errors, convergence rates and CPU times are included for four and 11 species.

scholarly journals A Three-Stage Fifth-Order Runge-Kutta Method for Directly Solving Special Third-Order Differential Equation with Application to Thin Film Flow Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
M. Mechee ◽  
N. Senu ◽  
F. Ismail ◽  
B. Nikouravan ◽  
Z. Siri
Keyword(s):  
Thin Film ◽  
Differential Equation ◽  
Film Flow ◽  
New Method ◽  
Kutta Method ◽  
Thin Film Flow ◽  
Third Order ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Fifth Order

In this paper, a three-stage fifth-order Runge-Kutta method for the integration of a special third-order ordinary differential equation (ODE) is constructed. The zero stability of the method is proven. The numerical study of a third-order ODE arising in thin film flow of viscous fluid in physics is discussed. The mathematical model of thin film flow has been solved using a new method and numerical comparisons are made when the same problem is reduced to a first-order system of equations which are solved using the existing Runge-Kutta methods. Numerical results have clearly shown the advantage and the efficiency of the new method.

A Fifth-order Symplectic Trigonometrically Fitted Partitioned Runge-Kutta Method

2007 ◽  
Author(s):  
Z. Kalogiratou ◽  
Th. Monovasilis ◽  
T. E. Simos ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
...  
Keyword(s):  
Kutta Method ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Fifth Order

scholarly journals Accurate Numerical Method for Singular Initial-Value Problems

2021 ◽  
Vol 08 (03) ◽  
pp. 01-11
Author(s):  
Tesfaye Aga Bullo ◽  
Gemechis File Duressa ◽  
Gashu Gadisa Kiltu
Keyword(s):  
Numerical Method ◽  
Initial Value Problems ◽  
Approximate Solutions ◽  
Stability And Convergence ◽  
Order System ◽  
Kutta Method ◽  
Initial Value ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Fifth Order

In this paper, an accurate numerical method is presented to find the numerical solution of the singular initial value problems. The second-order singular initial value problem under consideration is transferred into a first-order system of initial value problems, and then it can be solved by using the fifth-order Runge Kutta method. The stability and convergence analysis is studied. The effectiveness of the proposed methods is confirmed by solving three model examples, and the obtained approximate solutions are compared with the existing methods in the literature. Thus, the fifth-order Runge-Kutta method is an accurate numerical method for solving the singular initial value problems.

scholarly journals Study of Numerical Solution of Fourth Order Ordinary Differential Equations by fifth order Runge-Kutta Method

2019 ◽  
pp. 230-238
Author(s):  
Najmuddin Ahamad ◽  
Shiv Charan
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fourth Order ◽  
Initial Value Problems ◽  
Computational Cost ◽  
Kutta Method ◽  
Initial Value ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Fifth Order

In this paper we present fifth order Runge-Kutta method (RK5) for solving initial value problems of fourth order ordinary differential equations. In this study RK5 method is quite efficient and practically well suited for solving boundary value problems. All mathematical calculation performed by MATLAB software for better accuracy and result. The result obtained, from numerical examples, shows that this method more efficient and accurate. These methods are preferable to some existing methods because of their simplicity, accuracy and less computational cost involved.

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