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math.NA2020★ 12 cited
Numerical Computation of Solitary Wave Solutions of the Rosenau Equation
H. A. Erbay, S. Erbay, A. Erkip
We construct numerically solitary wave solutions of the Rosenau equation using the Petviashvili iteration method. We first summarize the theoretical results available in the litera…
math.NA2019★ 8 cited
A semi-discrete numerical method for convolution-type unidirectional wave equations
H. A. Erbay, S. Erbay, A. Erkip
Numerical approximation of a general class of nonlinear unidirectional wave equations with a convolution-type nonlocality in space is considered. A semi-discrete numerical method b…
math.NA2018
Convergence of a Semi-Discrete Numerical Method for a Class of Nonlocal Nonlinear Wave Equations
H. A. Erbay, S. Erbay, A. Erkip
In this article, we prove the convergence of a semi-discrete numerical method applied to a general class of nonlocal nonlinear wave equations where the nonlocality is introduced th…