A semi-discrete numerical scheme for nonlocally regularized KdV-type equations

Name: A semi-discrete numerical scheme for nonlocally regularized KdV-type equations
Author: Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.

İsim	A semi-discrete numerical scheme for nonlocally regularized KdV-type equations
Yazar	Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.
Basım Tarihi:	2022-05
Basım Yeri	- Elsevier
Konu	Discretization, Error estimates, KdV equation, Nonlocal nonlinear wave equation, Rosenau equation, Semi-discrete scheme
Tür	Süreli Yayın
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	0168-9274
Kayıt Numarası	c51e24a9-4471-4d93-a746-c99c1e492f7f
Lokasyon	Natural and Mathematical Sciences
Tarih	2022-05
Örnek Metin	A general class of KdV-type wave equations regularized with a convolution-type nonlocality in space is considered. The class differs from the class of the nonlinear nonlocal unidirectional wave equations previously studied by the addition of a linear convolution term involving third-order derivative. To solve the Cauchy problem we propose a semi-discrete numerical method based on a uniform spatial discretization, that is an extension of a previously published work of the present authors. We prove uniform convergence of the numerical method as the mesh size goes to zero. We also prove that the localization error resulting from localization to a finite domain is significantly less than a given threshold if the finite domain is large enough. To illustrate the theoretical results, some numerical experiments are carried out for the Rosenau-KdV equation, the Rosenau-BBM-KdV equation and a convolution-type integro-differential equation. The experiments conducted for three particular choices of the kernel function confirm the error estimates that we provide.
DOI	10.1016/j.apnum.2022.02.003
Cilt	175

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A semi-discrete numerical scheme for nonlocally regularized KdV-type equations

Yazar Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.

Basım Tarihi 2022-05

Basım Yeri - Elsevier

Konu Discretization, Error estimates, KdV equation, Nonlocal nonlinear wave equation, Rosenau equation, Semi-discrete scheme

Tür Süreli Yayın

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 0168-9274

Kayıt Numarası c51e24a9-4471-4d93-a746-c99c1e492f7f

Lokasyon Natural and Mathematical Sciences

Tarih 2022-05

Örnek Metin A general class of KdV-type wave equations regularized with a convolution-type nonlocality in space is considered. The class differs from the class of the nonlinear nonlocal unidirectional wave equations previously studied by the addition of a linear convolution term involving third-order derivative. To solve the Cauchy problem we propose a semi-discrete numerical method based on a uniform spatial discretization, that is an extension of a previously published work of the present authors. We prove uniform convergence of the numerical method as the mesh size goes to zero. We also prove that the localization error resulting from localization to a finite domain is significantly less than a given threshold if the finite domain is large enough. To illustrate the theoretical results, some numerical experiments are carried out for the Rosenau-KdV equation, the Rosenau-BBM-KdV equation and a convolution-type integro-differential equation. The experiments conducted for three particular choices of the kernel function confirm the error estimates that we provide.

DOI 10.1016/j.apnum.2022.02.003

Cilt 175