Septic B-Spline Collocation Method for the Numerical Solution of the Modified Equal Width Wave Equation

Abstract

Numerical solutions of the modified equal width wave equation are obtained by using collocation method with septic B-spline finite elements with three different linearization techniques. The motion of a single solitary wave, interaction of two solitary waves and birth of solitons are studied using the proposed method. Accuracy of the method is discussed by computing the numerical conserved laws error norms L2 and L∞. The numerical results show that the present method is a remarkably successful numerical technique for solving the MEW equation. A linear stability analysis shows that this numerical scheme, based on a Crank Nicolson approximation in time, is unconditionally stable.

Numerical solutions of the modified equal width wave equation are obtained by using collocation method with septic B-spline finite elements with three different linearization techniques. The motion of a single solitary wave, interaction of two solitary waves and birth of solitons are studied using the proposed method. Accuracy of the method is discussed by computing the numerical conserved laws error norms L2 and L∞. The numerical results show that the present method is a remarkably successful numerical technique for solving the MEW equation. A linear stability analysis shows that this numerical scheme, based on a Crank Nicolson approximation in time, is unconditionally stable.

Cite this paper

nullT. Geyikli and S. Karakoc, "Septic B-Spline Collocation Method for the Numerical Solution of the Modified Equal Width Wave Equation,"*Applied Mathematics*, Vol. 2 No. 6, 2011, pp. 739-749. doi: 10.4236/am.2011.26098.

nullT. Geyikli and S. Karakoc, "Septic B-Spline Collocation Method for the Numerical Solution of the Modified Equal Width Wave Equation,"

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