Spectral Collocation Methods for Second-Order Volterra Integro-Differential Equations with Weakly Singular Kernels

Advances in Applied Mathematics and Mechanics ◽

10.4208/aamm.oa-2019-0056 ◽

2020 ◽

Vol 12 (2) ◽

pp. 480-502

Author(s):

Xiulian Shi

Keyword(s):

Differential Equations ◽

Second Order ◽

Collocation Methods ◽

Spectral Collocation ◽

Weakly Singular Kernels ◽

Weakly Singular ◽

Singular Kernels ◽

Spectral Collocation Methods

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Spectral Collocation Methods for Nonlinear Volterra Integro-Differential Equations with Weakly Singular Kernels

Bulletin of the Malaysian Mathematical Sciences Society ◽

10.1007/s40840-017-0487-7 ◽

2017 ◽

Vol 42 (1) ◽

pp. 297-314 ◽

Author(s):

Yin Yang ◽

Yanping Chen

Keyword(s):

Differential Equations ◽

Collocation Methods ◽

Spectral Collocation ◽

Weakly Singular Kernels ◽

Weakly Singular ◽

Singular Kernels ◽

Spectral Collocation Methods

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Collocation methods for fractional integro-differential equations with weakly singular kernels

Numerical Algorithms ◽

10.1007/s11075-013-9710-2 ◽

2013 ◽

Vol 65 (4) ◽

pp. 723-743 ◽

Author(s):

Jingjun Zhao ◽

Jingyu Xiao ◽

Neville J. Ford

Keyword(s):

Differential Equations ◽

Collocation Methods ◽

Weakly Singular Kernels ◽

Weakly Singular ◽

Singular Kernels

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An $hp$-version Legendre-Jacobi spectral collocation method for Volterra integro-differential equations with smooth and weakly singular kernels

Mathematics of Computation ◽

10.1090/mcom/3183 ◽

2017 ◽

Vol 86 (307) ◽

pp. 2285-2324 ◽

Author(s):

Zhong-qing Wang ◽

Yu-ling Guo ◽

Li-jun Yi

Keyword(s):

Differential Equations ◽

Collocation Method ◽

Spectral Collocation Method ◽

Spectral Collocation ◽

Weakly Singular Kernels ◽

Weakly Singular ◽

Singular Kernels ◽

Jacobi Spectral Collocation Method

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An $hp$-Version of $C^0$ -Continuous Petrov-Galerkin Time-Stepping Method for Second-Order Volterra Integro-Differential Equations with Weakly Singular Kernels

East Asian Journal on Applied Mathematics ◽

10.4208/eajam.020520.120620 ◽

2021 ◽

Vol 11 (1) ◽

pp. 20-42

Author(s):

Shuangshuang Li

Keyword(s):

Differential Equations ◽

Second Order ◽

Weakly Singular Kernels ◽

Time Stepping ◽

Weakly Singular ◽

Singular Kernels

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A note on collocation methods for Volterra integro-differential equations with weakly singular kernels

IMA Journal of Numerical Analysis ◽

10.1093/imanum/13.1.93 ◽

1993 ◽

Vol 13 (1) ◽

pp. 93-99 ◽

Author(s):

TAO TANG

Keyword(s):

Differential Equations ◽

Collocation Methods ◽

Weakly Singular Kernels ◽

Weakly Singular ◽

Singular Kernels

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Spectral collocation methods for nonlinear weakly singular Volterra integro-differential equations

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22314 ◽

2018 ◽

Vol 35 (2) ◽

pp. 576-596 ◽

Author(s):

Xiulian Shi ◽

Yunxia Wei ◽

Fenglin Huang

Keyword(s):

Differential Equations ◽

Collocation Methods ◽

Spectral Collocation ◽

Weakly Singular ◽

Spectral Collocation Methods

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An hp-Version Chebyshev Spectral Collocation Method for Nonlinear Volterra Integro-Differential Equations with Weakly Singular Kernels

Numerical Mathematics Theory Methods and Applications ◽

10.4208/nmtma.oa-2018-0104 ◽

2019 ◽

Vol 12 (3) ◽

pp. 969-994

Author(s):

Hongli Jia

Keyword(s):

Differential Equations ◽

Collocation Method ◽

Spectral Collocation Method ◽

Spectral Collocation ◽

Weakly Singular Kernels ◽

Weakly Singular ◽

Chebyshev Spectral Collocation ◽

Singular Kernels ◽

Chebyshev Spectral Collocation Method

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Convergence Analysis of the Legendre Spectral Collocation Methods for Second Order Volterra Integro-Differential Equations

Numerical Mathematics Theory Methods and Applications ◽

10.4208/nmtma.2011.m1028 ◽

2011 ◽

Vol 4 (3) ◽

pp. 419-438 ◽

Author(s):

Yunxia Wei and Yanping Chen

Keyword(s):

Differential Equations ◽

Convergence Analysis ◽

Second Order ◽

Collocation Methods ◽

Spectral Collocation ◽

Spectral Collocation Methods

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Piecewise Polynomial Collocation Methods for Linear Volterra Integro-Differential Equations with Weakly Singular Kernels

SIAM Journal on Numerical Analysis ◽

10.1137/s0036142900376560 ◽

2001 ◽

Vol 39 (3) ◽

pp. 957-982 ◽

Author(s):

Hermann Brunner ◽

Arvet Pedas ◽

Gennadi Vainikko

Keyword(s):

Differential Equations ◽

Collocation Methods ◽

Piecewise Polynomial ◽

Weakly Singular Kernels ◽

Weakly Singular ◽

Singular Kernels ◽

Polynomial Collocation

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Euler wavelets method for solving fractional-order linear Volterra–Fredholm integro-differential equations with weakly singular kernels

Computational and Applied Mathematics ◽

10.1007/s40314-021-01565-9 ◽

2021 ◽

Vol 40 (6) ◽

Author(s):

S. Behera ◽

S. Saha Ray

Keyword(s):

Differential Equations ◽

Fractional Order ◽

Weakly Singular Kernels ◽

Order Linear ◽

Weakly Singular ◽

Singular Kernels

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