Runge-Kutta Integration of the Equal Width Wave Equation Using the Method of Lines

Banaja M. A.; Bakodah H. O.

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Runge-Kutta Integration of the Equal Width Wave Equation Using the Method of Lines

机译：等距波动方程线法的Runge-Kutta积分

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The equal width (EW) equation governs nonlinear wave phenomena like waves in shallow water. Numerical solution of the (EW) equation is obtained by using the method of lines (MOL) based on Runge-Kutta integration. Using von Neumann stability analysis, the scheme is found to be unconditionally stable. Solitary wave motion and interaction of two solitary waves are studied using the proposed method. The three invariants of the motion are evaluated to determine the conservation properties of the generated scheme. Accuracy of the proposed method is discussed by computing the L-2 and L-infinity error norms. The results are found in good agreement with exact solution.

机译：等宽（EW）方程控制着非线性波浪现象，例如浅水中的波浪。通过基于Runge-Kutta积分的直线法（MOL）获得（EW）方程的数值解。使用冯·诺依曼稳定性分析，发现该方案是无条件稳定的。利用所提出的方法研究了孤立波的运动以及两个孤立波的相互作用。评估运动的三个不变量以确定所生成方案的守恒性质。通过计算L-2和L-无穷大误差范数讨论了所提出方法的准确性。发现结果与精确解决方案非常吻合。

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《Mathematical Problems in Engineering》 |2015年第12期|274579.1-274579.9|共9页
作者
Banaja M. A.; Bakodah H. O.;
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King Abdulaziz Univ, Sci Fac Girls, Dept Math, Jeddah 21589, Saudi Arabia.;

King Abdulaziz Univ, Sci Fac Girls, Dept Math, Jeddah 21589, Saudi Arabia.;

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1. Runge-Kutta Integration of the Equal Width Wave Equation Using the Method of Lines [J] . M. A.Banaja, H. O.Bakodah Mathematical Problems in Engineering: Theory, Methods and Applications . 2015,第2期

机译：等距波动方程线法的Runge-Kutta积分
2. Runge-Kutta Integration of the Equal Width Wave Equation Using the Method of Lines [J] . M. A.Banaja, H. O.Bakodah Mathematical Problems in Engineering: Theory, Methods and Applications . 2015,第1期

机译：等距波动方程线法的Runge-Kutta积分
3. Application of Hes Exp-function method and semi-inverse variational principle to equal width wave (EW) and modified equal width wave (MEW) equations [J] . H. A. Ali, A. Biswas, K. R. Raslan International Journal of Physical Sciences . 2012,第7期

机译：Hes Exp函数法和半逆变分原理在等宽波（EW）和修正等宽波（MEW）方程中的应用
4. Numerical solution of the equal width wave equation using the method of lines [C] . S. Hamdi, J. J. Gottlieb, J. S. Hansen CFD Society of Canada . 2002

机译：使用线路的等宽波方程的数值解
5. Numerical solutions of the equal width wave equation using an adaptive method of lines. [D] . Hamdi, Samir. 2002

机译：等宽波方程的线型自适应解。
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Runge-Kutta Integration of the Equal Width Wave Equation Using the Method of Lines

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