NONPOLYNOMIAL CUBIC SPLINE APPROXIMATION FOR THE EQUAL WIDTH EQUATION

Abstract

In this paper, we investigate the numerical solutions of the equal width (EW) equation via the nonpolynomial cubic spline functions. Crank- Nicolson formulas are used for time discretization of the target equation. A linearization technique is also employed for the numerical purpose. Accuracy of the method is observed by the pointwise rate of convergence. Stability of the suggested method is investigated via the von-Neumann analysis. Six numerical examples related to single solitary wave, interaction of two, three and opposite waves, wave undulation and the Maxwell wave are considered as the test problems. The accuracy and the eciency of the purposed method are measured by L1 and L2 error norms and conserved constants. The obtained results are compared with the possible analytical values and those in some earlier studies.

Keywords

• EW equation; Nonpolynomial spline; Solitary waves

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