Volterra integral equations with highly oscillatory kernels: A new numerical method with applications

被引:0
作者
Fermo L. [1 ]
van der Mee C. [1 ]
机构
[1] Department of Mathematics and Computer Science, University of Cagliari, Via Ospedale 72
来源
Electronic Transactions on Numerical Analysis | 2021年 / 54卷
关键词
Highly oscillatory kernels; Korteweg-de Vries equation; Mixed quadrature scheme; Nyström method; Volterra integral equation;
D O I
10.1553/ETNA_VOL54S333
中图分类号
学科分类号
摘要
The aim of this paper is to present a Nyström-type method for the numerical approximation of the solution of Volterra integral equations of the second kind having highly oscillatory kernels. The method is based on a mixed quadrature scheme which combines the classical product rule with a dilation quadrature formula. The convergence and the stability of the method are investigated and the accuracy of the presented approach is assessed by some numerical tests. The proposed procedure is also applied to the computation of initial scattering data related to the initial value problem associated to the Korteweg-de Vries equation. Copyright © 2021, Kent State University.
引用
收藏
页码:333 / 354
页数:21
相关论文
共 50 条
[31]   A new numerical approximation for Volterra integral equations combining two quadrature rules [J].
Mennouni, Abdelaziz .
APPLIED MATHEMATICS AND COMPUTATION, 2011, 218 (05) :1962-1969
[32]   Analysis of Generalized Multistep Collocation Solutions for Oscillatory Volterra Integral Equations [J].
Chen, Hao ;
Liu, Ling ;
Ma, Junjie .
MATHEMATICS, 2020, 8 (11) :1-16
[33]   Frequency-explicit convergence analysis of collocation methods for highly oscillatory Volterra integral equations with weak singularities [J].
Ma, Junjie ;
Kang, Hongchao .
APPLIED NUMERICAL MATHEMATICS, 2020, 151 :1-12
[34]   Numerical Based Solution of Nonlinear Volterra Integral Equations Using Laplace Decomposition Method [J].
Shone, T. T. ;
Patra, Ashrita ;
Mishra, B. B. .
ADVANCEMENTS IN MATHEMATICS AND ITS EMERGING AREAS, 2020, 2214
[35]   Numerical solution of Volterra integral equations via Szasz-Mirakyan approximation method [J].
Usta, Fuat ;
Ilkhan, Merve ;
Evren Kara, Emrah .
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (09) :7491-7500
[36]   A new approach to the numerical solution of Volterra integral equations by using Bernstein's approximation [J].
Maleknejad, K. ;
Hashemizadeh, E. ;
Ezzati, R. .
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2011, 16 (02) :647-655
[37]   Differential transform method for solving Volterra integral equation with separable kernels [J].
Odibat, Zaid M. .
MATHEMATICAL AND COMPUTER MODELLING, 2008, 48 (7-8) :1144-1149
[38]   Recursive higher order fuzzy transform method for numerical solution of Volterra integral equation with singular and nonsingular kernels [J].
Zeinali, Masoumeh ;
Bahrami, Fariba ;
Shahmorad, Sedaghat .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2022, 403
[39]   An efficient method for solving system of Volterra integral equations [J].
Nouni, Kazem .
KYBERNETES, 2012, 41 (3-4) :501-507
[40]   Composite quadrature rules for a class of weakly singular Volterra integral equations with noncompact kernels [J].
Majidian, Hassan .
APPLIED NUMERICAL MATHEMATICS, 2014, 83 :1-11