A Spectral Method for Second Order Volterra Integro-Differential Equation with Pantograph Delay

AbstractIn this paper, a Legendre-collocation spectral method is developed for the second order Volterra integro-differential equation with pantograph delay. We provide a rigorous error analysis for the proposed method. The spectral rate of convergence for the proposed method is established in both L2-norm and L∞-norm.

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Maximal Regularity Results for a Second Order Integro-differential Equation

Journal of Mathematical Analysis and Applications ◽

10.1006/jmaa.1995.1127 ◽

1995 ◽

Vol 191 (2) ◽

pp. 203-228 ◽

Cited By ~ 3

Author(s):

D. Sforza

Keyword(s):

Differential Equation ◽

Maximal Regularity ◽

Second Order ◽

Integro Differential Equation ◽

Regularity Results

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A spectral method for approximate solving a second-order linear differential equation

Journal of Physics Conference Series ◽

10.1088/1742-6596/973/1/012057 ◽

2018 ◽

Vol 973 ◽

pp. 012057 ◽

Cited By ~ 2

Author(s):

M N Oreshina

Keyword(s):

Differential Equation ◽

Linear Differential Equation ◽

Spectral Method ◽

Second Order ◽

Order Linear Differential Equation ◽

Order Linear ◽

Linear Differential

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Convergence Analysis of Legendre-Collocation Spectral Methods for Second Order Volterra Integro-Differential Equation with Delay

Advances in Applied Mathematics and Mechanics ◽

10.4208/aamm.oa-2018-0121 ◽

2019 ◽

Vol 11 (2) ◽

pp. 486-500

Author(s):

Weishan Zheng

Keyword(s):

Differential Equation ◽

Convergence Analysis ◽

Spectral Methods ◽

Second Order ◽

Integro Differential Equation ◽

Equation With Delay

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An efficient spectral method and rigorous error analysis based on dimension reduction scheme for fourth order problems

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22523 ◽

2020 ◽

Vol 37 (1) ◽

pp. 152-171

Author(s):

Lan Li ◽

Jing An

Keyword(s):

Error Analysis ◽

Dimension Reduction ◽

Spectral Method ◽

Fourth Order ◽

Reduction Scheme ◽

Rigorous Error ◽

Fourth Order Problems

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ON BARBASHIN NONLINEAR INTEGRO-DIFFERENTIAL EQUATION WITH PARTIAL DERIVATIVE OF THE SECOND ORDER

Far East Journal of Mathematical Sciences (FJMS) ◽

10.17654/ms102112587 ◽

2017 ◽

Vol 102 (11) ◽

pp. 2587-2598

Author(s):

A. S. Kalitvin ◽

V. A. Kalitvin

Keyword(s):

Differential Equation ◽

Partial Derivative ◽

Second Order ◽

Integro Differential Equation

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Electrogravitational stability of streaming compound jets

International Journal of Biomathematics ◽

10.1142/s1793524516500327 ◽

2016 ◽

Vol 09 (02) ◽

pp. 1650032 ◽

Cited By ~ 2

Author(s):

Alfaisal A. Hasan

Keyword(s):

Differential Equation ◽

Electric Field ◽

Second Order ◽

Integro Differential Equation

The electrohydrodynamic stability of a self-gravitating streaming compound jet has been investigated for all modes of perturbation. The jets are immersed in a dielectric motionless tenuous medium pervaded by varying electric field. A second-order integro-differential equation of Mathieu type has been derived and some reported works are recovered as limiting cases from it.

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